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Large characteristic subgroups satisfying multilinear commutator identities
Author(s) -
Khukhro E. I.,
Makarenko N. Yu.
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm047
Subject(s) - mathematics , multilinear map , commutator subgroup , commutator , fitting subgroup , bounded function , identity (music) , pure mathematics , automorphism , order (exchange) , combinatorics , group (periodic table) , class (philosophy) , finite group , discrete mathematics , normal subgroup , algebra over a field , p group , mathematical analysis , computer science , chemistry , lie conformal algebra , physics , organic chemistry , finance , artificial intelligence , acoustics , economics
It is proved that if a group G has a subgroup H of finite index n satisfying a multilinear commutator identity ϰ ( H ) = 1, then G has also a characteristic subgroup C satisfying the same identity ϰ ( C ) = 1 and having finite index bounded in terms of n and the weight of ϰ. 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 γ 3 ( S ).
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