I know that a group H has exactly one 3-Sylow subgroup L. Also, |H|=30. And |M|=15 is normal. Now I should consider the quotient group H/M and prove that . And then that each element of odd order in H is in M. Can someone help me please?
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Originally Posted by HoneyPi I know that a group H has exactly one 3-Sylow subgroup L. Also, |H|=30. And |M|=15 is normal. Now I should consider the quotient group H/M and prove that . And then that each element of odd order in H is in M. Can someone help me please? For (1): Lemma: if , then ( for the proof use Lagrange in the quotient ) For (2): Use directly Lagrange and (1). Tonio
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