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Alex
Frequent VisitorJoined: 03 Nov 2003Posts: 22
Location: CUHK
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Posted: Fri Sep 24, 2004 1:14 am Post subject: An Algebra Problem(2)
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[tex]Let be a group of order . Suppose that half of the elements of are of order 2, and the other half form a subgroup of order . Prove that is of odd order and is an abelian subgroup of .
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Siutsz
Frequent VisitorJoined: 25 Dec 2003Posts: 31
Location: HK
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Posted: Fri Sep 24, 2004 2:38 pm Post subject:
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, then .
,
,
, so is abelian.
Suppose is even, say , then
, , a contradiction.
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