Alternatives for pseudofinite groups

作者：Houcine Abderezak Ould^*; Point Francoise

来源：Journal of Group Theory, 2013, 16(4): 461-495.

DOI：10.1515/jgt-2013-0006

The famous Tits alternative states that a linear group either contains a non-abelian free group or is soluble-by-(locally finite). In this paper we study similar alternatives in pseudofinite groups. We show, for instance, that an aleph(0)-saturated pseudofinite group either contains a subsemigroup of rank 2 or is nilpotent-by-(uniformly locally finite). We call a class of finite groups G weakly of bounded rank if the radical rad(G) has a bounded Prufer rank and the index of the socle of G/rad(G) is bounded. We show that an aleph(0)-saturated pseudo-(finite weakly of bounded rank) group either contains a non-abelian free group or is nilpotent-by-abelian-by-(uniformly locally finite). We also obtain some relations between these kind of alternatives and amenability.

• 出版日期2013-7