Let w be a group word. It is conjectured that if w has only countably many values in a profinite group G, then the verbal subgroup w(G) is finite. In the present paper we confirm the conjecture in the cases where w is a multilinear commutator word, or the word x2, or the word [x2, y].
On conciseness of words in profinite groups / Detomi, Eloisa; Morigi, Marta; Shumyatsky, Pavel. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - STAMPA. - 220:8(2016), pp. 3010-3015. [10.1016/j.jpaa.2016.02.003]
On conciseness of words in profinite groups
MORIGI, MARTA;
2016
Abstract
Let w be a group word. It is conjectured that if w has only countably many values in a profinite group G, then the verbal subgroup w(G) is finite. In the present paper we confirm the conjecture in the cases where w is a multilinear commutator word, or the word x2, or the word [x2, y].File in questo prodotto:
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