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

Marciniak, Zbigniew; Sehgal, Sudarshan

doi:10.1090/proc/16249

Constructing free products of cyclic subgroups inside the group of units of integral group rings
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by Zbigniew Marciniak and Sudarshan K. Sehgal

Proc. Amer. Math. Soc. 151 (2023), 1487-1493

DOI: https://doi.org/10.1090/proc/16249

Published electronically: January 30, 2023

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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.

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