Given a group-word w and a group G, the verbal subgroup w(G) is the one generated by all w-values in G. The word w is said to be boundedly concise if for each positive integer m there exists a number depending only on m and w bounding the order of w(G) whenever the set of w-values in a group G has size at most m. In the present article we show that various generalizations of the Engel word are boundedly concise in residually finite groups.

On bounded conciseness of Engel-like words in residually finite groups

Morigi M.;
2019

Abstract

Given a group-word w and a group G, the verbal subgroup w(G) is the one generated by all w-values in G. The word w is said to be boundedly concise if for each positive integer m there exists a number depending only on m and w bounding the order of w(G) whenever the set of w-values in a group G has size at most m. In the present article we show that various generalizations of the Engel word are boundedly concise in residually finite groups.
Detomi E.; Morigi M.; Shumyatsky P.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/714254
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