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WORDS AND PRONILPOTENT SUBGROUPS IN PROFINITE GROUPS

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups Representation theory of groups

Published online by Cambridge University Press:  29 September 2014

E. I. KHUKHRO  and
P. SHUMYATSKY
E. I. KHUKHRO*
Affiliation:
Sobolev Institute of Mathematics, Novosibirsk 630 090, Russia email [email protected]
P. SHUMYATSKY
Affiliation:
Department of Mathematics, University of Brasilia, Brasilia DF 70910-900, Brazil email [email protected]
*
✉[email protected]
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Abstract

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Let $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}w$ be a multilinear commutator word, that is, a commutator of weight $n$ in $n$ different group variables. It is proved that if $G$ is a profinite group in which all pronilpotent subgroups generated by $w$-values are periodic, then the verbal subgroup $w(G)$ is locally finite.

Keywords

profinite groupslocally finitecommutatorpronilpotentperiodic

MSC classification

Secondary: 20E18: Limits, profinite groups 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure 20F50: Periodic groups; locally finite groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 97 , Issue 3 , December 2014 , pp. 343 - 364
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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