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LEFT MAXIMAL AND STRONGLY RIGHT MAXIMAL IDEMPOTENTS IN G*

Published online by Cambridge University Press:  21 March 2017

YEVHEN ZELENYUK
YEVHEN ZELENYUK*
Affiliation:
SCHOOL OF MATHEMATICS UNIVERSITY OF THE WITWATERSRAND PRIVATE BAG 3, WITS 2050 SOUTH AFRICAE-mail: yevhen.zelenyuk@wits.ac.za
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Abstract

Let G be a countably infinite discrete group, let βG be the Stone–Čech compactification of G, and let ${G^{\rm{*}}} = \beta G \setminus G$. An idempotent $p \in {G^{\rm{*}}}$ is left (right) maximal if for every idempotent $q \in {G^{\rm{*}}}$, pq = p (qp = P) implies qp = q (qp = q). An idempotent $p \in {G^{\rm{*}}}$ is strongly right maximal if the equation xp = p has the unique solution x = p in G*. We show that there is an idempotent $p \in {G^{\rm{*}}}$ which is both left maximal and strongly right maximal.

Keywords

Primary 22A1554H20Secondary 54D8054H11Stone–Čechcompactificationultrafilterprincipal left idealorbit closureleft maximal idempotentstrongly right maximal idempotent
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 1 , March 2017 , pp. 26 - 34
Copyright
Copyright © The Association for Symbolic Logic 2017 

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