Finitely generated soluble groups with an Engel condition on infinite subsets

Abstract

In this note, we prove that, in every finitely generated soluble group G, G/Z2 (G) is finite if and only if in every infinite subset X of G there exist different x, y such that [x, y, y] = 1. © Rendiconti del Seminario Matematico della Università di Padova, 2000, tous droits réservés.