*-simple groups without free subgroups
Alexander Yu. Olshanskii
Vanderbilt University, Nashville, United StatesDenis Osin
Vanderbilt University, Nashville, United States
Abstract
We construct first examples of non-trivial groups without non-cyclic free subgroups whose reduced -algebra is simple and has unique trace. This answers a question of de la Harpe. Both torsion and torsion free examples are provided. In particular, we show that the reduced -algebra of the free Burnside group of rank and any sufficiently large odd exponent is simple and has unique trace.
Cite this article
Alexander Yu. Olshanskii, Denis Osin, *-simple groups without free subgroups. Groups Geom. Dyn. 8 (2014), no. 3, pp. 933–983
DOI 10.4171/GGD/253