Alternating units as free factors in the group of units of integral group rings

Abstract

Let G be a group of odd order that contains a non-central element x whose order is either a prime p 5 or 3 l , with l 2. Then, in U (ZG), the group of units of ZG, we can find an alternating unit u based on x, and another unit v, which can be either a bicyclic or an alternating unit, such that for all sufficiently large integers m we have that u m , v m = u m * v m ∼ = Z * Z.