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

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 obtaine...

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Bibliographic Details
Published in:Sbornik. Mathematics 2009-06, Vol.200 (5)
Main Authors: Klyachko, Anton A, Mel'nikova, Yuliya B
Format: Article
Language:English
Subjects:
COMMUTATORS
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
GROUP THEORY
INDEXES
MATHEMATICAL METHODS AND COMPUTING
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Summary: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.
ISSN:1064-5616
1468-4802
DOI:10.1070/SM2009V200N05ABEH004013;COUNTRYOFINPUT:INTERNATIONALATOMICENERGYAGENCY(IAEA)