New article in group theory


Associate Professor Nick Gill has had his paper "A generalization of a theorem of Rodgers and Saxl for simple groups of bounded rank" accepted for publication in the Bulletin of the London Mathematical Society. The paper is joint work with Laszlo Pyber and Endre Szabo of the Renyi Institute, Budapest.

The paper is in the area of group theory. It considers the problem of taking a finite simple group G, and a sequence of subsets of G, call them A_1,...., A_k, and asks when it is possible to write G=A_1^{g_1}... A_k^{g_k}, for some g_1,..., g_k in G. In other words this is a question about writing a group as a "product of conjugates of subsets of itself".

This question, which sounds very technical and abstract, has interesting connections to other areas of mathematics. In particular, it fits within the general study of GROWTH in a finite group, results in which have had connections to expander graphs, efficient networking and number-theoretic sieving.