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WORDS AND PRONILPOTENT SUBGROUPS IN PROFINITE GROUPS
Part of
E. I. KHUKHRO, P. SHUMYATSKY
Journal:

Journal of the Australian Mathematical Society / Volume 97 / Issue 3 / December 2014

Published online by Cambridge University Press:

29 September 2014, pp. 343-364

Print publication:

December 2014
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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.