Let w be a group-word. Given a group G, we denote by w(G) the verbal subgroup corresponding to the word w, that is, the subgroup generated by the set G(w) of all w-values in G. The word w is called concise in a class of groups X if w(G) is finite whenever G(w) is finite for a group G is an element of chi. It is a long-standing problem whether every word is concise in the class of residually finite groups. In this paper we examine several families of group-words and show that all words in those families are concise in residually finite groups.

Bounding the order of a verbal subgroup in a residually finite group

Morigi M.;
2023

Abstract

Let w be a group-word. Given a group G, we denote by w(G) the verbal subgroup corresponding to the word w, that is, the subgroup generated by the set G(w) of all w-values in G. The word w is called concise in a class of groups X if w(G) is finite whenever G(w) is finite for a group G is an element of chi. It is a long-standing problem whether every word is concise in the class of residually finite groups. In this paper we examine several families of group-words and show that all words in those families are concise in residually finite groups.
2023
Detomi E.; Morigi M.; Shumyatsky P.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/933973
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