On Finitely Presented Groups that Contain Q

Abstract: It is a consequence of Higman's embedding theorem that the additive group Q of rational numbers can be embedded into a finitely presented group. Though Higman's proof is constructive, the resulting group presentation would be very large and ungainly. In 1999, Martin Bridson and Pierre de la Harpe asked for an explicit and "natural" example of a finitely presented group that contains an embedded copy of Q. In this talk, we describe some solutions to this problem related to Thompson's groups F, T, and V, including a new simple group of type F infinity that contains Q. This is joint work with James Hyde and Francesco Matucci.

algebraic topologydifferential geometrygeneral topologygroup theorygeometric topology

Audience: researchers in the topic

Ohio State Topology and Geometric Group Theory Seminar

Series comments: https://sites.google.com/view/topoandggt