On finiteness of verbal subgroups

Jo\~ao Azevedo; Pavel Shumyatsky

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arxiv 2009.10121 v2 pith:HVCOWQQE submitted 2020-09-21 math.GR

On finiteness of verbal subgroups

Jo\~ao Azevedo , Pavel Shumyatsky This is my paper

classification math.GR

keywords concisedotsfiniteverbalwordconjecturedenotedfiniteness

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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 $[u_1,\dots,u_s]$ is concise whenever the words $u_1,\dots,u_s$ are non-commutator.

On finiteness of verbal subgroups

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