Cheryl Praeger

Diagonal structures and primitive permutation groups

Many maximal subgroups of finite symmetric groups arise as stabilisers of some structure on the point set: for example the maximal intransitive permutation groups are subset stabilisers. The primitive groups of diagonal type for a long time have seemed exceptional in this respect. Csaba Schneider and I have introduced diagonal structures which, for the first time, give a combinatorial interpretation to these primitive groups of simple diagonal type. In further work together also with Peter Cameron and Rosemary Bailey, we’ve exhibited these groups as automorphism groups of `diagonal graphs’.