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 βG∖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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm150-12-2015,
author = {Yevhen Zelenyuk},
title = {Almost maximal topologies on groups},
journal = {Fundamenta Mathematicae},
volume = {233},
year = {2016},
pages = {91-100},
zbl = {06602783},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm150-12-2015}
}
Yevhen Zelenyuk. Almost maximal topologies on groups. Fundamenta Mathematicae, Tome 233 (2016) pp. 91-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm150-12-2015/