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On the order of the commutator subgroup and the Schur multiplier of a finitep-group

Authors
Journal
Journal of Algebra
0021-8693
Publisher
Elsevier
Publication Date
Volume
144
Issue
2
Identifiers
DOI: 10.1016/0021-8693(91)90106-i

Abstract

Abstract Green [ Proc. Roy. Soc. Math A 327 (1956) , 574–581] proved that if G is a finite p-group of order p n and M( G) is its Schur multiplier of order p m( G) , then m(G) ⩽ 1 2 n(n − 1) . We consider, among other things, the case when m(G) = 1 2 n(n − 1) and then prove that if this equality holds, then G = E( p n ), that is, G is an elementary abelian group of order p n .

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