Constructing free products of cyclic subgroups inside the group of units of integral group rings

Abstract:

It has been proved in Janssens, Jespers, and Temmerman [Proc. Amer. Math. Soc. 145 (2017), pp. 2771–2783] that if $h$ is an element of prime order $p$ in a finite nilpotent group $G$ and $u=h+(h-1)g\widehat {h}\in \mathbb {Z}G$, $u\not \in G$, then $\langle u^*,u\rangle \approx C_p\ast C_p$. We offer a simple geometric approach to generalize this result.