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]. © 2016 Elsevier B.V.
On conciseness of words in profinite groups
DETOMI, ELOISA MICHELA;
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]. © 2016 Elsevier B.V.
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