Paper:KhuMak07

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Large characteristic subgroups satisfying multilinear commutator identities by Evgenii I. Khukhro and N. Yu. Makarenko, Journal of the London Mathematical Society, July 2007, Page 1-12: This proves that if a group has a subgroup of finite index satisfying a multilinear commutator identity, then we can find a characteristic subgroup of finite index satisfying the same identity. The result is used to prove facts about fixed point-free automorphisms on nilpotent groups