SEMINAR: Groups and Combinatorics Seminar: Triple factorisations: geometric approach

Groups and Combinatorics Seminar

Hassan Alavi (UWA)

will speak on

Triple factorisations: geometric approach

at 1pm Tuesday 3rd of August in MLR2

Abstract:

Triple factorisations G = ABA, for proper subgroups A and B of a group G, are fundamental in the study of Lie type groups, as well as in geometry. They correspond to flag-transitive collinearly connected point-line geometries (in which each pair of points lies on at least one line). Geometries satisfying the dual condition -where each pair of lines meets in at least one point- are called concurrently connected. In this talk, we consider a generalisation of point-line projective geometries called (m,k,j)-projective spaces and determine when they are collinearly and/or concurrently connected. These geometrical results arose from studying triple factorisations of general linear groups G with the subgroups A and B parabolic.



All welcome.