Geodesic
A short proof of the Khukhro-Makarenko theorem on large characteristic subgroups with laws
Sbornik. Mathematics, Tome 200 (2009) no. 5, pp. 661-664

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We give a short proof and a somewhat stronger version of the Khukhro-Makarenko theorem that each group which virtually satisfies an outer commutator identity contains a finite-index characteristic subgroup satisfying this identity. An estimate for the index of this characteristic subgroup is obtained. Bibliography: 3 titles.
Keywords: characteristic subgroups, outer commutator identities. 
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     title = {A short proof of the {Khukhro-Makarenko} theorem on large characteristic subgroups with laws},
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A. A. Klyachko; Yu. B. Mel'nikova. A short proof of the Khukhro-Makarenko theorem on large characteristic subgroups with laws. Sbornik. Mathematics, Tome 200 (2009) no. 5, pp. 661-664. http://geodesic.mathdoc.fr/item/SM_2009_200_5_a1/