dr. Primož Potočnik – Group amalgams and locally arc-transitive graphs

19.12.2011 Lecturer: dr. Primož Potočnik (University of Ljubljana, Slovenia)

Title: Group amalgams and locally arc-transitive graphs.

Abstract: A group amalgam is a quintuple (L,f,B,g,R) where L,B and R are abstract groups and f:B->L and g:B->R are group monomorphisms. Given a connected locally G-arc-transitive graph X (ie. a connected graph X together with a group of automorphisms G of X such that the vertex-stabiliser G_v is transitive on the neighbourhood of v in X for every vertex v of X), one can consider the amalgam (G_v,f,G_uv,g,G_u) where f and g are the inclusion mappings. Conversely, given an amalgam (satisfying certain additional requirements), one can construct all connected locally arc-transitive graphs up to a given number of vertices that realises the amalgam. This interplay of amalgams and graphs will be described in the talk in some (but not too many) details.