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Journal of the London Mathematical Society Advance Access originally published online on July 11, 2007
Journal of the London Mathematical Society 2007 75(3):635-646; doi:10.1112/jlms/jdm047
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© 2007 London Mathematical Society

Large characteristic subgroups satisfying multilinear commutator identities

E. I. Khukhro1, and N. Yu. Makarenko2

1 School of Mathematics
Cardiff University
Cardiff CF24 4AG
United Kingdom
2 Institute of Mathematics
Novosibirsk 630090
Russia
natalia_makarenko{at}yahoo.fr

It is proved that if a group G has a subgroup H of finite index n satisfying a multilinear commutator identity {varkappa} (H) = 1, then G has also a characteristic subgroup C satisfying the same identity {varkappa} (C) = 1 and having finite index bounded in terms of n and the weight of {varkappa}. 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 {gamma}3(S).

khukhro{at}cardiff.ac.uk

2000 Mathematics Subject Classification 20E07 (primary), 20D45 (secondary).

This work was supported by the ‘Universities of Russia’ grant UR.04.01.202.

Received September 6, 2006; published online July 11, 2007.


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