Alternatives for pseudofinite groups
Group Theory
2012-05-17 v1 Logic
Abstract
The famous Tits' alternative states that a linear group either contains a nonabelian free group or is soluble-by-(locally finite). We study in this paper similar alternatives in pseudofinite groups. We show for instance that an -saturated pseudofinite group either contains a subsemigroup of rank or is nilpotent-by-(uniformly locally finite). We call a class of finite groups weakly of bounded rank if the radical has a bounded Pr\"ufer rank and the index of the sockel of is bounded. We show that an -saturated pseudo-(finite weakly of bounded rank) group either contains a nonabelian free group or is nilpotent-by-abelian-by-(uniformly locally finite). We also obtain some relations between this kind of alternatives and amenability.
Cite
@article{arxiv.1205.3533,
title = {Alternatives for pseudofinite groups},
author = {Abderezak Ould Houcine and Françoise Point},
journal= {arXiv preprint arXiv:1205.3533},
year = {2012}
}