Almost maximal topologies on groups

Yevhen Zelenyuk¹

¹ School of Mathematics University of the Witwatersrand Private Bag 3, Wits 2050 Johannesburg, South Africa

Fundamenta Mathematicae, Tome 234 (2016) no. 1, pp. 91-100

Résumé

Let $G$ be a countably infinite group. We show that for every finite absolute coretract $S$, there is a regular left invariant topology on $G$ whose ultrafilter semigroup is isomorphic to $S$. As consequences we prove that (1) there is a right maximal idempotent in $\beta G\setminus G$ which is not strongly right maximal, and (2) for each combination of the properties of being extremally disconnected, irresolvable, and nodec, except for the combination $(-,-,+)$, there is a corresponding regular almost maximal left invariant topology on $G$.

Détail

DOI : 10.4064/fm150-12-2015

Keywords: countably infinite group every finite absolute coretract there regular invariant topology whose ultrafilter semigroup isomorphic consequences prove there right maximal idempotent beta setminus which strongly right maximal each combination properties being extremally disconnected irresolvable nodec except combination there corresponding regular almost maximal invariant topology nbsp