A condition on a certain variety of groups

Abstract

Let α1,…, αn be nonzero integers whose greatest common divisor is d. We prove that an infinite group G is of finite exponent dividing d if and only if for every n infinite subsets X1, …, Xn of G there exist x1 ∈ X1, …, xn ∈ Xn such that x1α1…xαnn = 1. © Rendiconti del Seminario Matematico della Università di Padova, 2000, tous droits réservés.