On finiteness of verbal subgroups

2020/09/21 by Azevedo, João, Shumyatsky, Pavel
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2009.10121

Abstract

Given a group-word w and a group G, the set of w-values in G is denoted by G_w and the verbal subgroup w(G) is the one generated by G_w. The word w is concise if w(G) is finite for all groups G in which G_w is finite. We obtain several results supporting the conjecture that the word [u₁,…,u_s] is concise whenever the words u₁,…,u_s are non-commutator.

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