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. (2019). On bounded conciseness of Engel-like words in residually finite groups. JOURNAL OF ALGEBRA, 521, 1-15 [10.1016/j.jalgebra.2018.11.020].
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.File in questo prodotto:
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