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Idempotents in $\beta G\setminus G$ with only trivial divisors

Volume 248 / 2020

Yevhen Zelenyuk 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 $a\in G$.

Authors

  • Yevhen ZelenyukSchool of Mathematics
    University of the Witwatersrand
    Private Bag 3, Wits 2050
    Johannesburg, South Africa
    e-mail

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