试证：若[tex=2.357x1.357]5c345lWEq6hWYLbA1o+QkQ==[/tex]是阿贝尔群，则对任意[tex=2.714x1.214]sSIApBg6OzoLyhTiB5OMxw==[/tex]必有[tex=5.429x1.857]giJt87JwCJzZpuPemFvCerB1g8phUQBOE5KovI7mAbw=[/tex].
举一反三
- 试证：若[tex=2.357x1.357]j8rDlXbx/BSYHmc34GKijQ==[/tex]是可换群,则对任意[tex=2.857x1.214]sSIApBg6OzoLyhTiB5OMxw==[/tex] 必有[tex=6.143x1.357]giJt87JwCJzZpuPemFvCetEFq2ImMamwp9BfZ74s8R8=[/tex]
- [tex=2.357x1.357]HLbOsiEJc4IlAkVLNRXl3Q==[/tex]是阿贝尔群，[tex=2.714x1.214]hFofrIH8bsnX+Pd+KhTmrw==[/tex]，[tex=0.571x0.786]WLga5RWgrUta8vWDwROpYA==[/tex]的阶为7，[tex=0.429x1.0]dX3JVuFw9r8t2KlWf+/Z+A==[/tex]的阶为5，则[tex=1.5x1.0]eZtVfYia3vQ8SVjhmElGew==[/tex]的阶为（ ）. 未知类型：{'options': ['7', '35', '12', '5'], 'type': 102}
- 证明,一个群[tex=0.786x1.0]JTRtgqQ00R3dUQzwS4iwbg==[/tex]是阿贝尔群的充要条件是:对于任意[tex=2.714x1.214]sSIApBg6OzoLyhTiB5OMxw==[/tex]和任意整数[tex=0.643x0.786]SBMIs+VUk7//BOpfqlQl0w==[/tex]都有[tex=4.429x1.929]h6kzfXCttC+oUENc/9nb8U+7o+MRd9e0DHvkkhLO6BOoNkfVPtVvlb6PJRzcKGd2[/tex]
- 设[tex=2.357x1.357]tivK2mu6Un99R8QaBwhvzDm113TWvWVM+IuiJLKOwk8=[/tex]是有限可交换独异点，若对于所有的[tex=4.143x1.214]AAU2YpehMeyzHhfnLSpJLg==[/tex]，有[tex=6.929x1.0]SxgU0aP4YpZi+9rzJsv0+zMMCxkAtdtH++s81uVL4WA=[/tex]。试证明[tex=2.357x1.357]tivK2mu6Un99R8QaBwhvzDm113TWvWVM+IuiJLKOwk8=[/tex]是一个阿贝尔群。
- 判断下列命题是否为真：（1）[tex=3.643x1.357]/5abqJjwKZ1qr+6hsVFF5EBvfq3ggOFNlHMClz0h9nk=[/tex]（2）[tex=2.929x1.357]rGJpyjIjJpbcoBTWxP0Jiw==[/tex]（3）[tex=4.5x1.357]2wycHMoqU83MyEp17iBils58bR7YLuCTI2G9NVAdlfY=[/tex]（4）[tex=5.214x1.357]CTz2gu+IIm1GgNmYMGaduCRtA41wnW4WqwRWwEhq6aA=[/tex]（5）[tex=4.857x1.357]1DcE2BMMOaZhTuxR/mjgsboXxfg5ET59Dp4I/jjEDuw=[/tex]（6）[tex=4.643x1.357]BSryrsQYOvTP2hTWRu6t4nAuJwlSs4L9jaq70EpB+Us=[/tex]（7）若[tex=6.0x1.357]y0IZLUnBO88nR8WBZYvd7QXv5S1OMINV5cQNzPyiyAc=[/tex]，则[tex=3.429x1.357]1brfPwTkVVIX4GfoMIUskA==[/tex]（8）若[tex=7.643x1.357]MhLfJXZnhbXiB0x3oNtFzThV4Y1mJxe1VYr7PkJE/T6hmTD3WWp+UxbNwvUQ6DHk[/tex]，则[tex=4.143x1.357]LZUA94ISo1po5HWsOVeBCjo0rMvj7uw3bGw5HiZenrI=[/tex]