Large characteristic subgroups satisfying multilinear commutator identities

Khukhro, E. I. and Makarenko, N. Y. (2007) Large characteristic subgroups satisfying multilinear commutator identities. Journal of the London Mathematical Society, 75 (3). pp. 635-646. ISSN 0024-6107

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Item Type:Article
Item Status:Live Archive

Abstract

It is proved that if a group G has a subgroup H of finite index n satisfying a multilinear commutator identity (H) = 1, then G has also a characteristic subgroup C satisfying the same identity (C) = 1 and having finite index bounded in terms of n and the weight of . As an illustration, the result on characteristic subgroups is applied to a finite group with an almost regular automorphism of order 4 to obtain a subgroup S of bounded index with a 'strong' bound for the nilpotency class of γ3(S). © 2007 London Mathematical Society.

Additional Information:First published online: July 11, 2007
Keywords:Group theory
Subjects:G Mathematical and Computer Sciences > G100 Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:15598
Deposited On:31 Oct 2014 15:50

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