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

Abstract

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 $\mathcal{U}(\mathbb{Z}G)$ , the group of units of ℤ G , 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

Locations

• Proceedings of the Edinburgh Mathematical Society - View - PDF