Given a group-word w and a group G, the verbal subgroup w(G) is the one generated by all w-values in G. Thewordw is said to be concise if w(G) is finite whenever the set of w-values in G is finite. In 1960s, Hall asked whether every word is concise but later Ivanov answered this question in the negative. On the other hand, Hall’s question remains wide open in the class of residually finite groups. In the present paper we show that various generalizations of the Engel word are concise in residually finite groups.
Detomi E., Morigi M., Shumyatsky P. (2019). Words of Engel type are concise in residually finite groups. BULLETIN OF MATHEMATICAL SCIENCES, 9(2), 1-19 [10.1142/S1664360719500127].
Words of Engel type are concise 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. Thewordw is said to be concise if w(G) is finite whenever the set of w-values in G is finite. In 1960s, Hall asked whether every word is concise but later Ivanov answered this question in the negative. On the other hand, Hall’s question remains wide open in the class of residually finite groups. In the present paper we show that various generalizations of the Engel word are concise in residually finite groups.| File | Dimensione | Formato | |
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