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Permutation groups and cartesian decompositions

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Group theory and generalizations; Topological groups, lie groups; Algebraic structures

video/mp4

Author affiliation: Universidade Federal de Minas Gerais

2017-05-15

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61673

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/