If is a group of odd order, show for any nonidentity element that and are not conjugate in . Definition: and are conjugates if for some .
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Originally Posted by dori1123 If is a group of odd order, show for any nonidentity element that and are not conjugate in . Definition: and are conjugates if for some . If then (taking the inverse of both sides) . Therefore , , and in fact whenever n is odd (including when n is equal to the order of G)...
Originally Posted by Opalg If then (taking the inverse of both sides) . Therefore , , and in fact whenever n is odd (including when n is equal to the order of G)... I don't understand how does this show that and are not conjugates when is odd?
If then (the identity), so , or . That in turn means that .
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