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.File in questo prodotto:
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