Let be a finite group of odd order and Prove that is not conjugate to
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Suppose .......... (1) Then Combining with (1) : So But since is odd, . In particular we find such that . This yields , so commute and .
Last edited by Bruno J.; Jul 2nd 2009 at 03:38 PM.
Originally Posted by Bruno J. Suppose .......... (1) Then Combining with (1) : So But since is odd, . In particular we find such that . This yields , so commute and . you can also use induction to show that for all odd numbers and then choose to get and thus
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