Large characteristic subgroups satisfying multilinear commutator identities

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