Residual properties of Generalized Baumslag-Solitar groups

Abstract: For a group G let γω(G) denote the intersection of the lower central series and (Np)ω(G) denote the intersection of all subgroups whose index is a power of a prime p. The group G is residually nilpotent if and only if γω(G) is trivial while G is a residually finite p-group if and only if (Np)ω(G) is trivial. Thus, the groups γω(G) and (Np)ω(G) describe how far G is from being residually nilpotent and being a residually finite p-group respectively. In this talk we will describe the Generalized Baumslag-Solitar groups (GBS groups) which are fundamental groups of graphs of groups with infinite cyclic vertex and edge groups and then we will compute the intersections γω(G) and (Np)ω(G) in the case where the underlying graph is a tree. The results presented are based on joint work with V. Metaftsis.

Mathematics

Audience: researchers in the topic

Greek Algebra & Number Theory Seminar