The Tits alternative for non-spherical Pride groups
by Dr. Natasha Kopteva
Abstract: Pride groups, or "groups given by presentations in which each defining relator involves at most two types of generators", include Coxeter groups, Artin groups, triangles of groups, and Vinberg's groups defined by periodic paired relations. A Pride group is presented by a certain labelled graph. A group is said to satisfy the Tits alternative if it either contains a non-abelian free group or has a soluble subgroup of finite index. We show that every non-spherical Pride group based on a graph with at least four vertices satisfies the Tits alternative.
For More Information: Dr. Lawrence Reeves email: L.Reeves@ms.unimelb.edu.au