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arXiv · 1803.04202

BFC-theorems for higher commutator subgroups

Eloisa Detomi·Marta Morigi·Pavel Shumyatsky
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Abstract

A BFC-group is a group in which all conjugacy classes are finite with bounded size. In 1954 B. H. Neumann discovered that if G is a BFC-group then the derived group G' is finite. Let w=w(x_1,\dots,x_n) be a multilinear commutator. We study groups in which the conjugacy classes containing w-values are finite of bounded order. Let G be a group and let w(G) be the verbal subgroup of G generated by all w-values. We prove that if x^G has size at most m for every w-value x, then the derived subgroup of w(G) is finite of order bounded by a function of m and n. If x^{w(G)} has size at most m for every w-value x, then [w(w(G)),w(G)] is finite of order bounded by a function of m and n.

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Eloisa Detomi, Marta Morigi, Pavel Shumyatsky. 2018-03-12. BFC-theorems for higher commutator subgroups. https://arxiv.org/abs/1803.04202

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