Triple factorisations of finite groups!

Welcome to my weblog!

This is my first post on my blog and I would like to write about what I am doing in my PhD.

My research project is about triple factorisations of finite groups. Triple factorisations , for proper subgroups and of a group , correspond to fag-transitive point-line incidence geometries in which each pair of points is incident with at least one line. We initiate a general study of triple factorisations using the language and theory of group actions. We obtain two criteria for triple factorisations (Theorem 1.1 in [AP09]). This leads to an order (upper) bound for in terms of and (Theorem 1.3 in [AP09]). We also develop a reduction pathway to triple factorisations for which induces a primitive group action on the coset space of (Theorem 1.5 in [AP09]). This opens the way for applying powerful primitive permutation group theory to analyse such `point-primitive’ triple factorisations.

[AP09] (With Cheryl E. Praeger), On triple factorisations of finite groups, J. Group Theory, to appear DOI®