LOCALIZATION OF q-ABELIAN GROUPS

Abstract. Let q be a prime number. We prove that the (1/q)-localization of a q-abelian group (i.e. a group in which (xy)q = xqyq for all x, y) is again a q-abelian group. This provides an example of a class of groups which need not be nilpotent and behave well under localization. First we point out some facts on the structure of q-abelian groups and describe a simple procedure to obtain nontrivial examples. 1. Introduction. A group G in which (xy)n = xnyn holds for all elements x, y and some fixed integer n has been called n-abelian. This concept was first considered in [12] and extensively analyzed in [7], [2], [3], [1]. Most of the standard notation was introduced by R. Baer in [3]