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BIRS Workshop Lecture Videos

Permutation groups and cartesian decompositions Schneider, Csaba


Intransitive and imprimitive permutation groups preserve disjoint union decompositions and are routinely studied by considering their actions on invariant partitions. I would like to present a similar approach to the study of permutation groups that preserve cartesian product decompositions. Such groups occur naturally in the various versions of the O'Nan-Scott Theorem, and also in combinatorial applications, such as groups of automorphisms of Hamming graphs. Much of the theory I present is valid for arbitrary permutation groups. However, combining this theory with the classification of finite simple groups leads to a surprisingly detailed descriptions of finite groups that act on cartesian products. The results I present were obtained in collaboration with Robert Baddeley and Cheryl Praeger.

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