This article is cited in 14 papers

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

A. A. Klyachko, Yu. B. Mel'nikova

Faculty of Mechanics and Mathematics, M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 512.544.44+512.543.22+512.544.33

MSC: 20E36, 20F12, 20F16, 20F18, 20F19, 20E10

Received: 12.06.2008

DOI: 10.4213/sm6380

 English version: Sbornik: Mathematics, 2009, 200:5, 661–664

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