A short proof of the Khukhro--Makarenko theorem on large characteristic subgroups with laws

Abstract

We give a short proof and some strengthening of the Khukhro--Makarenko theorem that each group virtually satisfying an outer commutator identity contains a finite-index characteristic subgroup satisfying this identity. An estimate for the index of this characteristic subgroup is obtained.

2 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm . V2: the bound is corrected

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