21秋福师《近世代数》考前练兵百分

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发表于 2021-10-14 09:55:42 | 显示全部楼层 |阅读模式
《近世代数》考前练兵
1.[单选题] 设<img id="ODzfrtuTEMP20200329035349964.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODzfrtuTEMP20200329035349964.png?Expires=1900828430&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=t6MXo4J4X8P/bKMV3FSufT6uTTg%3D" />,则<img id="ODuwpcxTEMP20200329035350142.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODuwpcxTEMP20200329035350142.png?Expires=1900828430&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=2Y4bn09o1oLMe1Ho4IfZQTWPjsE%3D" /> (   )

    A.<img id="ODdjjolTEMP20200329035350285.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODdjjolTEMP20200329035350285.png?Expires=1900828430&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=bDvH60HXqSTcJAXF16niJ0wS%2BGI%3D" />
    B.<img id="ODcjdnaTEMP20200329035350432.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODcjdnaTEMP20200329035350432.png?Expires=1900828430&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=DaYUre4fG2ijkwD1hXipSZAFb9c%3D" />
    C.<img id="ODqtxenTEMP20200329035350681.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODqtxenTEMP20200329035350681.png?Expires=1900828430&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=cvzTV4r/7nrjMhI1euC71NWIJWk%3D" />
    D.<img id="ODrwwviTEMP20200329035350835.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODrwwviTEMP20200329035350835.png?Expires=1900828431&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=SexMUBCLmcGUgOjdFA6wMn7M4W8%3D" />
    答:——D——
2.[单选题] <img id="ODqzepyTEMP20200329035351046.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODqzepyTEMP20200329035351046.png?Expires=1900828431&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=sSOzm8ZkzlhAPFzC2M2bdxSQBvc%3D" />的全体元素用循环置换的方法写出来就是( )
    A.(12),(23),(123),(132)
    B.(1),(23),(123),(132)
    C.(1),(12),(13),(23),(123),(132)
    D.(1),(12),(23),(123),(132)
    答:——C——
3.[单选题] 设<img id="ODdytinTEMP20200329035351219.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODdytinTEMP20200329035351219.png?Expires=1900828431&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=cAnmpScqrutdwfGWlbrljwUgeBY%3D" />,则<img id="ODxyzreTEMP20200329035351389.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODxyzreTEMP20200329035351389.png?Expires=1900828431&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=dnWZKGrYluGMX9GCmWB8nQrWLDY%3D" />( )
    A.<img id="ODvihppTEMP20200329035351440.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODvihppTEMP20200329035351440.png?Expires=1900828431&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=gGPpDjiw4Sxc1QYrJtv8bVq34O8%3D" />
    B.<img id="ODarxsvTEMP20200329035351611.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODarxsvTEMP20200329035351611.png?Expires=1900828431&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=KKEMl0JRZUbuZYa7ahzKg1aQn8g%3D" />
    C.<img id="ODmbwijTEMP20200329035351772.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODmbwijTEMP20200329035351772.png?Expires=1900828431&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=HHsAJLm/8pLmD3qYsRm4rItog%2B0%3D" />
    D.<img id="ODxepsvTEMP20200329035352085.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODxepsvTEMP20200329035352085.png?Expires=1900828432&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=aiAP8UV%2BO2fS6/r/I0Ch7EQBKI4%3D" />
    答:——C——
4.[单选题] 对于下面给出的整数集Z到整数集Z的映射<img id="ODwlcfpTEMP20200329035352237.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODwlcfpTEMP20200329035352237.png?Expires=1900828432&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=n28ewOAhHeATSqUc9Do/HpWPo3E%3D" /><img id="ODznpmwTEMP20200329035352292.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODznpmwTEMP20200329035352292.png?Expires=1900828432&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=B8VEASiDGRhgGXO5b6tsb4KDi%2BE%3D" />则<img id="ODzciwnTEMP20200329035352501.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODzciwnTEMP20200329035352501.png?Expires=1900828432&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=%2BbMJ4QNjixVmGJEfqgtTizl6KQY%3D" /><b>=</b><b>( )</b>
    A.<img id="ODntgerTEMP20200329035352764.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODntgerTEMP20200329035352764.png?Expires=1900828432&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=e6MMYMDGocj%2BIBHKG2IibHXUmak%3D" />
    B.<img id="ODimnjoTEMP20200329035352849.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODimnjoTEMP20200329035352849.png?Expires=1900828432&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=46aG5TQ2YgC%2BxL4Tm7mYF7CAtUA%3D" />
    C.<img id="ODbczkwTEMP20200329035353126.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODbczkwTEMP20200329035353126.png?Expires=1900828433&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=ElSI29Kvf2brsjRk5Zs4keV%2BrDQ%3D" />
    D.<img id="ODvjbmoTEMP20200329035353290.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODvjbmoTEMP20200329035353290.png?Expires=1900828433&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=VOc1Donhv%2BLCecTFLNHMAa9brC0%3D" />
    答:————
5.[单选题] <img id="ODxavayTEMP20200329035353367.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODxavayTEMP20200329035353367.png?Expires=1900828433&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=7Uf7aJOvrfhCRQE8/bGXjQBUQ7E%3D" /><b>( )</b>
    A.(12)(34)
    B.(1234)
    C.(123)(4)
    D.(3)(124)
    答:————
6.[单选题] 设(Z,+)是整数加群,<img id="ODmpmliTEMP20200329035353628.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODmpmliTEMP20200329035353628.png?Expires=1900828433&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=uymWzGk7XInOq2%2BySTVO2B1%2Bmes%3D" />,求[Z:H]=( )
    A.2
    B.3
    C.4
    D.5
    答:————
7.[单选题] 设<img id="ODbskwhTEMP20200329035353682.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODbskwhTEMP20200329035353682.png?Expires=1900828433&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=Wx1q/CbkY0T0KoJWs7E8YgxpOB8%3D" />,则<img id="ODynaxiTEMP20200329035353920.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODynaxiTEMP20200329035353920.png?Expires=1900828434&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=4Wiq0QZvrIx7uIzfvVLx46fT7CI%3D" /> (   )
    A.<img id="ODxmpaoTEMP20200329035353984.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODxmpaoTEMP20200329035353984.png?Expires=1900828434&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=bxLsfAJsMTbLUh9d8HOci0JE3NU%3D" />
    B.<img id="ODmvkdeTEMP20200329035354241.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODmvkdeTEMP20200329035354241.png?Expires=1900828434&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=A/iyR/cAHeh6wS3bIRmlqLyxpOo%3D" />
    C.<img id="ODyeqvxTEMP20200329035354388.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODyeqvxTEMP20200329035354388.png?Expires=1900828434&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=Dwo%2BGCF292VDs6UuifG1JdQMVno%3D" />
    D.<img id="ODfymexTEMP20200329035354547.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODfymexTEMP20200329035354547.png?Expires=1900828434&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=s3BUEo2M/SkHBML%2B/Weins8W3Hk%3D" />
    答:————
8.[单选题] 设<img id="ODldqsdTEMP20200329035354603.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODldqsdTEMP20200329035354603.png?Expires=1900828434&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=gneuour86zArf0GpwBq%2BykyBUHg%3D" />,则<img id="ODqcoksTEMP20200329035354764.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODqcoksTEMP20200329035354764.png?Expires=1900828434&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=P5cPt0w7hwKaz8q9RUbZhYr7ZbQ%3D" />()
    A.>
    B.</b><img id="ODpikjwTEMP20200329035355005.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODpikjwTEMP20200329035355005.png?Expires=1900828435&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=alZ6Zy7kCEWnXEqPTP%2BEJX9Yy%2BQ%3D" /><br><b>
    C.</b><img id="ODzpsqfTEMP20200329035355162.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODzpsqfTEMP20200329035355162.png?Expires=1900828435&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=DGW86S8UoAGuY411POJeAGCwMuk%3D" /><br><b>
    D.</b><img id="ODuzawbTEMP20200329035355328.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODuzawbTEMP20200329035355328.png?Expires=1900828435&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=DYB%2BXeUBqfD11XWzBpQFSr0Su1E%3D" /><br><b>
    E.</b><img id="ODdkfgnTEMP20200329035355374.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODdkfgnTEMP20200329035355374.png?Expires=1900828435&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=klqIZCxZiJvxoFd12y6ZDdzld8U%3D" />
    答:————
9.[单选题] 对于下面给出的整数集Z到整数集Z的映射<img id="ODilqulTEMP20200329035355532.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODilqulTEMP20200329035355532.png?Expires=1900828435&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=lzBHdwjaS146AEmSWuBH8FbjQA0%3D" /><img id="ODedyqkTEMP20200329035355793.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODedyqkTEMP20200329035355793.png?Expires=1900828435&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=wojYD4BX/54ZIufpItA2c%2B9E4Yg%3D" />则<img id="ODjhocoTEMP20200329035355969.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODjhocoTEMP20200329035355969.png?Expires=1900828436&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=wVU3DMOkFpSnk83CDwHrijZRMkw%3D" /><b>=</b><b>()</b>
    A.<img id="ODihlchTEMP20200329035356126.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODihlchTEMP20200329035356126.png?Expires=1900828436&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=ys%2BDNBjS4IGrgeMWlLnMj65n5TM%3D" />
    B.<img id="ODyiajuTEMP20200329035356179.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODyiajuTEMP20200329035356179.png?Expires=1900828436&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=pSK0whfLAAgG9nXGrYe8dNaFYM4%3D" />
    C.<img id="ODlvrfvTEMP20200329035356339.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODlvrfvTEMP20200329035356339.png?Expires=1900828436&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=7RWVimxCqVA2OSTOKQOIhUxIS%2Bs%3D" />
    D.<img id="ODapdmfTEMP20200329035356491.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODapdmfTEMP20200329035356491.png?Expires=1900828436&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=WiGqL2lkpU7CZD0KGTOdTEhikc8%3D" />
    答:————
10.[单选题] <img id="ODtmddfTEMP20200329035356655.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODtmddfTEMP20200329035356655.png?Expires=1900828436&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=nPad16Jip2vGFleJdI99hNEo8gw%3D" /> (    )
    A.(12)(34)
    B.(1234)
    C.(123)(4)
    D.(3)(124)
    答:————
11.[单选题] <img id="ODbxvpmTEMP20200329035356812.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODbxvpmTEMP20200329035356812.png?Expires=1900828437&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=rDi9UfZACL2kFUxIBm8hwQPxlCs%3D" />的全体元素用循环置换的方法写出来就是()
    A.(12),(23),(123),(132)
    B.(1),(23),(123),(132)
    C.(1),(12),(23),(123),(132)
    D.(1),(12),(13),(23),(123),(132)
    答:————
12.[单选题] 在整环Z中,6的真因子是()
    A.<img id="ODdbiuzTEMP20200329035356969.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODdbiuzTEMP20200329035356969.png?Expires=1900828437&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=9oLb08eZB4Vv%2BMiSlo4RSkpYKjs%3D" />
    B.<img id="ODmjeqvTEMP20200329035357249.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODmjeqvTEMP20200329035357249.png?Expires=1900828437&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=RBbUSzvfx1Qdffuz/QtU2njQASk%3D" />
    C.<img id="ODrbyjzTEMP20200329035357309.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODrbyjzTEMP20200329035357309.png?Expires=1900828437&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=a9crtlRtHwjrhdBqxMxDzAZ7YhM%3D" />
    D.<img id="ODhfanmTEMP20200329035357457.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODhfanmTEMP20200329035357457.png?Expires=1900828437&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=ZQbDnjh/p5MoIATqu04JO5juQyU%3D" />
    答:————
13.[判断题] 对称群一定不是交换群
    A.对
    B.错
    答:————
14.[判断题] 子群关于同一元素的左陪集与右陪集可能相等。
    A.对
    B.错
    答:————
15.[判断题] 已知<img id="ODwefmkTEMP20200329035342325.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODwefmkTEMP20200329035342325.png?Expires=1900828422&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=4RLh1mU/ika/bnNZ21stOwANHTo%3D" />是6阶群,则<img id="ODwmsisTEMP20200329035342628.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODwmsisTEMP20200329035342628.png?Expires=1900828423&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=K24Tyt6AMCxNNIpHvGRUTzlG37E%3D" />可能存在4阶子群。
    A.对
    B.错
    答:————
16.[判断题] 设<img id="ODrpxhaTEMP20200329035343080.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODrpxhaTEMP20200329035343080.png?Expires=1900828423&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=7g9xXvnvdIsCSqgI61B%2BLzQTMf4%3D" />是有单位元的交换环,<img id="ODdzdpqTEMP20200329035343247.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODdzdpqTEMP20200329035343247.png?Expires=1900828423&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=HMqdpM0stmb5XH9ri7kyKFMuUqg%3D" />是<img id="ODbvydvTEMP20200329035343422.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODbvydvTEMP20200329035343422.png?Expires=1900828423&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=qGGyLC7W6aqt9CFXmb8hWkyHkLU%3D" />的理想,则<img id="ODwhgqrTEMP20200329035343503.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODwhgqrTEMP20200329035343503.png?Expires=1900828423&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=Gso67DIFHNbk0XOpuuEAGEY96nw%3D" />是域。
    A.对
    B.错
    答:————
17.[判断题] 环中理想的和还是理想。
    A.对
    B.错
    答:————
18.[判断题] 4元置换(1243)是偶置换
    A.对
    B.错
    答:————
19.[判断题] 有单位元的环中所有非零元全体可构成一个群。
    A.对
    B.错
    答:————
20.[判断题] 每一个n元置换表示成对换乘积的对换个数奇偶性不变
    A.对
    B.错
    答:————
21.[判断题] 设<img id="ODiekneTEMP20200329035343739.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODiekneTEMP20200329035343739.png?Expires=1900828423&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=nK1M9tymXBf3BE3OXVUPkZs2/Pg%3D" />和<img id="ODfgbnlTEMP20200329035344005.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODfgbnlTEMP20200329035344005.png?Expires=1900828424&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=AAJj84kRQ2joIjlBvS%2BcuZqe%2BF8%3D" />都是非空集合,而<img id="ODvwrdmTEMP20200329035344076.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODvwrdmTEMP20200329035344076.png?Expires=1900828424&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=dW%2BCbcphNqpPfy%2Bp1QAuw7XKuwI%3D" />是<img id="ODvknsqTEMP20200329035344226.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODvknsqTEMP20200329035344226.png?Expires=1900828424&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=MfAX8ra/4fYnLTm5w0NmpUsgpGE%3D" />到<img id="ODduwvaTEMP20200329035344510.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODduwvaTEMP20200329035344510.png?Expires=1900828424&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=QUD4t%2B6CWJ3B3P7u11HL71DJRIE%3D" />的一个映射,那么元<img id="ODvptlfTEMP20200329035344623.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODvptlfTEMP20200329035344623.png?Expires=1900828424&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=qeKEBuBrtKtwO1Mn/i3l3MWse7M%3D" />的象不唯一。
    A.对
    B.错
    答:————
22.[判断题] 设<img id="ODcqtbyTEMP20200329035344875.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODcqtbyTEMP20200329035344875.png?Expires=1900828424&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=odSf8nDBzVWkR/tDTItEd%2BehG/Y%3D" />是<img id="ODkoexlTEMP20200329035344955.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODkoexlTEMP20200329035344955.png?Expires=1900828425&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=dtli4vfi6MWIrkSGuwjuVN%2BuDiA%3D" />的子群,若对于<img id="ODytgyvTEMP20200329035345202.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODytgyvTEMP20200329035345202.png?Expires=1900828425&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=OztDj9f%2BpkB48yKFtQZp0Djy17Y%3D" />,<img id="ODkratpTEMP20200329035345249.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODkratpTEMP20200329035345249.png?Expires=1900828425&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=v84Qo40%2BSa%2BxwEe9tBsl4oZisDw%3D" />,有<img id="ODjdbdlTEMP20200329035345508.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODjdbdlTEMP20200329035345508.png?Expires=1900828425&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=twHZjbpMKEWQm6Tubb%2BsWK/LDZ4%3D" />,则<img id="ODbyjwmTEMP20200329035345664.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODbyjwmTEMP20200329035345664.png?Expires=1900828425&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=iMMCblLqBOJCGzzvh2YpFPu6o5s%3D" />是<img id="ODwrislTEMP20200329035345712.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODwrislTEMP20200329035345712.png?Expires=1900828425&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=2dZM/VokFSD1D2Qh%2B1JDxpNi1Tc%3D" />的正规子群。
    A.对
    B.错
    答:————
23.[判断题] 整环中,既约元一定是素元
    A.对
    B.错
    答:————
24.[判断题] 设<img id="ODysektTEMP20200329035345878.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODysektTEMP20200329035345878.png?Expires=1900828426&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=m35Av80EP1BRhbr3MkRL/lqRHxs%3D" />是整数集,规定<img id="ODsvejzTEMP20200329035346136.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODsvejzTEMP20200329035346136.png?Expires=1900828426&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=rKfJbfMMfwCKzIuzBNyyOKPWvV0%3D" />,证明:<img id="ODnlytrTEMP20200329035346289.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODnlytrTEMP20200329035346289.png?Expires=1900828426&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=0pX18hAdoa%2BvcPr%2B67y%2BsrLFiQg%3D" />关于所定义的运算构成交换群
    A.对   
    B.错
    答:————
25.[判断题] 每一个n元置换都能写成若干个对换的乘积
    A.对
    B.错
    答:————
26.[判断题] 主理想环一定是欧氏环
    A.对
    B.错
    答:————
27.[判断题] 已知<img id="ODnebkkTEMP20200329035346364.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODnebkkTEMP20200329035346364.png?Expires=1900828426&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=LwynvDexhze6cQ1yYlmW3291w0U%3D" />是8阶群,则<img id="ODavsbyTEMP20200329035346530.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODavsbyTEMP20200329035346530.png?Expires=1900828426&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=JCbT1vErjgOJn006IjhcRqgfItY%3D" />可能存在5阶子群
    A.对
    B.错
    答:————
28.[判断题] 对称群<img id="ODbsvjgTEMP20200329035346792.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODbsvjgTEMP20200329035346792.png?Expires=1900828426&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=ACJ1iorpDfDydvS%2Bo3i46kFvVkg%3D" />中置换(1345)是偶置换。
    A.对
    B.错
    答:————
29.[判断题] 群中指数为2的子群一定是正规子群。
    A.对
    B.错
    答:————
30.[判断题] 已知<img id="ODjxqhzTEMP20200329035346951.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODjxqhzTEMP20200329035346951.png?Expires=1900828426&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=LQudVFW%2BWmQTVBuFxIpRS75WTRw%3D" />是有限群<img id="ODtwhhdTEMP20200329035347113.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODtwhhdTEMP20200329035347113.png?Expires=1900828427&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=Xaeb4TshAPaig%2BYTbYENXSVvCe8%3D" />的子群,<img id="ODjwhzsTEMP20200329035347196.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODjwhzsTEMP20200329035347196.png?Expires=1900828427&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=E0lUZaawSKNHelpQLVh0gGM23pQ%3D" />和<img id="ODpvnviTEMP20200329035347465.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODpvnviTEMP20200329035347465.png?Expires=1900828427&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=0Wm7TWZht3miRNcSShOjsTnSz6Q%3D" />分别表示<img id="ODkjzdzTEMP20200329035347640.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODkjzdzTEMP20200329035347640.png?Expires=1900828427&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=dDvV4Js2ZwOmi77z6U33wWC5NkA%3D" />和<img id="ODtbmdpTEMP20200329035347804.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODtbmdpTEMP20200329035347804.png?Expires=1900828427&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=PEGxTEmlRoIqckp35ntqWX2lmQw%3D" />的元素个数,则<img id="ODzxltzTEMP20200329035347964.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODzxltzTEMP20200329035347964.png?Expires=1900828427&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=6jueOCPlhBZeCR24udLvvwTQuTM%3D" />定能整除<img id="ODdkjtxTEMP20200329035348126.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODdkjtxTEMP20200329035348126.png?Expires=1900828428&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=lmnkx0vrm0MMQrgM/f8KdAUN3tU%3D" /><b>。</b>
    A.对
    B.错
    答:————
31.[判断题] 设<img id="ODnpzttTEMP20200329035348295.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODnpzttTEMP20200329035348295.png?Expires=1900828428&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=IG5Qwd8fS9M8WvmlFaP6q%2BWG8bg%3D" />是有单位元的交换环,<img id="ODithrbTEMP20200329035348349.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODithrbTEMP20200329035348349.png?Expires=1900828428&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=veKzQ3LMEMlChWR52d1GBNUgBrk%3D" />是<img id="ODyuvnqTEMP20200329035348529.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODyuvnqTEMP20200329035348529.png?Expires=1900828428&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=HMLdJvkVha%2BiDS2m2SeNhvYIVa4%3D" />的极大理想,则<img id="ODwkietTEMP20200329035348776.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODwkietTEMP20200329035348776.png?Expires=1900828428&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=mYtRBQ/TDoGHw2nusUQ/yhdwT6E%3D" />是域。
    A.对
    B.错
    答:————
32.[判断题] 环中极大理想的和还是极大理想。
    A.对
    B.错
    答:————
33.[判断题] 群<img id="ODhmglmTEMP20200329035348915.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODhmglmTEMP20200329035348915.png?Expires=1900828429&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=/TMTa6OIrRvIDQk/uCvsjaD1uco%3D" />关于子群<img id="ODqnamzTEMP20200329035348966.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODqnamzTEMP20200329035348966.png?Expires=1900828429&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=C8ckboTiC5ZXKkzE5m/FrE/ZrsY%3D" />的左陪集和右陪集个数不一定相等。
    A.对
    B.错
    答:————
34.[判断题] 剩余类加群Z12有6个生成元。
    A.对
    B.错
    答:————
35.[判断题] 设<img id="ODqeqppTEMP20200329035349153.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODqeqppTEMP20200329035349153.png?Expires=1900828429&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=zjv7DzI8zpsMOYU67vki0U29bvU%3D" />是整数集,规定<img id="ODitleiTEMP20200329035349332.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODitleiTEMP20200329035349332.png?Expires=1900828429&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=FWL/jKoUqiBnIFucUWjW5uH1240%3D" />,则<img id="ODonkdrTEMP20200329035349587.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODonkdrTEMP20200329035349587.png?Expires=1900828429&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=KBDnpCjlBRN/ZOvcxYaGt%2BTJYwc%3D" />关于所定义的运算构成交换群。
    A.对
    B.错
    答:————
36.[判断题] 整数集 QUOTE <img id="ODcwegfTEMP20200329035349743.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODcwegfTEMP20200329035349743.png?Expires=1900828429&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=7mosZLlnvPouu8OH008F6kr5N94%3D" /><img id="ODhlejbTEMP20200329035349801.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODhlejbTEMP20200329035349801.png?Expires=1900828430&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=MX/WVYSmWI5l/YFoiLPce9pRMJk%3D" />,按通常数的减法“-”运算,构成半群。
    A.对
    B.错
    答:————
37.[判断题] 两个左陪集的乘积是左陪集。
    A.对
    B.错
    答:————
38.[填空题] 每一个n元置换都能写成##对换的乘积。
    答:————
39.[填空题] 4元置换(1243)是##。
    答:————
40.[填空题] 设<img id="ODoatheTEMP20200329035357597.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODoatheTEMP20200329035357597.png?Expires=1900828437&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=gUGD4HEa36RsQ/34mBlnlHjJZfQ%3D" />,则<img id="ODakpayTEMP20200329035357745.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODakpayTEMP20200329035357745.png?Expires=1900828437&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=lJfSMsCwKiT2Uel3z6hlhEonsv4%3D" /><b> </b><b>##</b><b> </b>。
    答:————
41.[填空题] <img id="ODyqlpmTEMP20200329035358042.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODyqlpmTEMP20200329035358042.png?Expires=1900828438&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=CrYTPYiik%2BAfLxdiEgzzQnTC0O0%3D" />的全体元素用循环置换的方法写出来就是##。
    答:————
42.[问答题] 设<img id="ODehgfuTEMP20200329035358319.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODehgfuTEMP20200329035358319.png?Expires=1900828438&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=qiTjxIyFgHSpQkfkR/EMsZtJZsA%3D" />为素数,证明:<br>(1)对 QUOTE <img id="ODukliaTEMP20200329035358373.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODukliaTEMP20200329035358373.png?Expires=1900828438&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=p7xt8RjxqkUyWkb1doalYR%2BrH6I%3D" /><img id="ODwbvntTEMP20200329035358624.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODwbvntTEMP20200329035358624.png?Expires=1900828438&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=QcKa0RLhHvp9/y9u2QUMldtWj1k%3D" />,总有<img id="ODgkmcoTEMP20200329035358675.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODgkmcoTEMP20200329035358675.png?Expires=1900828438&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=U%2BIpqD74m95CIWO%2BVE5nQTQQcjA%3D" />;<br>(2)域 QUOTE <img id="ODivvtyTEMP20200329035358906.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODivvtyTEMP20200329035358906.png?Expires=1900828439&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=ICnGcNuG8sItpVhZkmjK8TPl0ls%3D" /><img id="ODxshdcTEMP20200329035359079.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODxshdcTEMP20200329035359079.png?Expires=1900828439&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=vJyGB6QbbcXZCpL4oSWGjf7oPAQ%3D" />中全部元是方程<img id="ODcinrfTEMP20200329035359139.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODcinrfTEMP20200329035359139.png?Expires=1900828439&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=LoMyfIWIDOdd98WAJULCnETGJug%3D" />的全部根。
    答:————
43.[问答题] 设<img id="ODynkdcTEMP20200329035402831.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODynkdcTEMP20200329035402831.png?Expires=1900828443&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=gnYN6jt9ADkr2/Lv//RrkV7iJpY%3D" />是交换群.证明: <img id="ODdhampTEMP20200329035403001.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODdhampTEMP20200329035403001.png?Expires=1900828443&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=cj8KBF2%2BUOJKMKSI8ZxK9IiJDRM%3D" />中所有阶数有限的元素的集合<img id="ODejcwkTEMP20200329035403152.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODejcwkTEMP20200329035403152.png?Expires=1900828443&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=G/Poc5eXWDT0moGnIbzC7Putw3w%3D" />按<img id="ODyhetgTEMP20200329035403393.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODyhetgTEMP20200329035403393.png?Expires=1900828443&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=%2BFIErwWitZQvNCsiLBulmijss60%3D" />的运算构成<img id="ODwmwezTEMP20200329035403545.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODwmwezTEMP20200329035403545.png?Expires=1900828443&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=my7IK%2B4q2%2BR%2B4EvrRVL2HmEh4TM%3D" />的正规子群
    答:————
44.[问答题] 求出模<img id="ODgroahTEMP20200329035404718.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODgroahTEMP20200329035404718.png?Expires=1900828444&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=3cQ/t6EDkQCJajPBR5uY7hWSAIA%3D" />剩余类环 QUOTE <img id="ODufhsjTEMP20200329035404871.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODufhsjTEMP20200329035404871.png?Expires=1900828445&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=k/d1Q/HqENrINo5zUlJsE9MJcWY%3D" /><img id="ODwyornTEMP20200329035405145.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODwyornTEMP20200329035405145.png?Expires=1900828445&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=g/6jQCjOK4/dRNJ5eyMswFErWeI%3D" />的所有理想和所有极大理想。
    答:————
45.[问答题] 若<img id="ODymzkqTEMP20200329035406234.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODymzkqTEMP20200329035406234.png?Expires=1900828446&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=%2Bt%2B65kARMLvf9bDwuY5ZdmLvgJU%3D" />的所有理想都由一个元生成,称<img id="ODtqvbpTEMP20200329035406400.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODtqvbpTEMP20200329035406400.png?Expires=1900828446&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=CO7dbCy2Nl0iUkPs0nYHSiCri0Y%3D" />为主理想整环。设<img id="ODgyrmaTEMP20200329035406486.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODgyrmaTEMP20200329035406486.png?Expires=1900828446&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=Hg3aRq9RtBvnq2epmJex2zsTOzY%3D" />是主理想整环,<img id="ODnosavTEMP20200329035407002.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODnosavTEMP20200329035407002.png?Expires=1900828447&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=0HvOGAsm/9DesTCZEOet0mzsZ0g%3D" />都是<img id="ODxwyazTEMP20200329035407063.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODxwyazTEMP20200329035407063.png?Expires=1900828447&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=8rMtmVevVEPO06Foo6zx2rtMoNw%3D" />的理想,如果对任意两个<img id="ODmkhyuTEMP20200329035407321.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODmkhyuTEMP20200329035407321.png?Expires=1900828447&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=PG%2B8TsbjLcdBDNjemMMB5qtf6a8%3D" />都有<img id="ODtrmtqTEMP20200329035407398.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODtrmtqTEMP20200329035407398.png?Expires=1900828447&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=1x0TvprNIbFB7jWC0QMYKyhQf4Y%3D" />或<img id="ODxpdkzTEMP20200329035407655.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODxpdkzTEMP20200329035407655.png?Expires=1900828447&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=2oDTNNwukFsV8Cw59JMe%2BCgM6Gk%3D" />,<br>证明:<img id="ODibsmuTEMP20200329035407703.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODibsmuTEMP20200329035407703.png?Expires=1900828447&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=CjQNa2BTStXCzKNIAnyjO5sjK9Q%3D" />是<img id="ODovsceTEMP20200329035407861.png" src="http://aseancdn.open.com.cn/zyglpt/OD/TEMP/2020/0329/ODovsceTEMP20200329035407861.png?Expires=1900828448&OSSAccessKeyId=gbI8DRLk7JJhLbEw&Signature=I4e/qXMp2KAnbgK2WukGFiVxu8M%3D" />的理想.
    答:————


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