On the exponent of a verbal subgroup in a finite group. (Q2840482)

A multilinear commutator in a free group is a word which is obtained by nesting commutators, but using always different indeterminates. The main result in this paper is Theorem 1.1: Let \(w\) be a multilinear commutator and \(G\) a finite group in which any nilpotent subgroup generated by \(w\)-values has exponent dividing \(e\). Then the exponent of the verbal group \(w(G)\) is bounded in terms of \(e\) and \(w\) only.NEWLINENEWLINE The case of Theorem 1.1 where \(w=[x,y]\) is an immediate corollary of the focal subgroup theorem, but the general case uses a number of sophisticated tools (such as the classification of finite simple groups and Zelmanov's solution of the restricted Burnside problem).