Idempotents in $\beta G\setminus G$ with only trivial divisors
Volume 248 / 2020
Fundamenta Mathematicae 248 (2020), 205-218
MSC: Primary 22A15, 54H11; Secondary 22A30, 54H20.
DOI: 10.4064/fm696-2-2019
Published online: 29 July 2019
Abstract
Let $G$ be a countably infinite discrete group, let $\beta G$ be the Stone–Čech compactification of $G$, and let $G^*=\beta G\setminus G$. We show that there is an idempotent $p\in G^*$ such that whenever $q,r\in G^*$ and $p=qr$, one has $q=pa$ and $r=a^{-1}p$ for some $a\in G$.
