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Finite permutation groups: applications to transformation semigroups and synchronization

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GRAW01 - Introductory/instructional workshop

For the last 10 years, I have been working with João Araújo and others on exploring how our new understanding of finite permutation groups can be used to advance the theory of finite transformation semigroups. In particular, I will talk about regularity and idempotent generation of semigroups, and synchronizing automata. The pioneering work had been done by semigroup theorists assuming that the transformation semigroup contains the symmetric or alternating group; but this assumption can be substantially weakened in many cases. (The first such result was a classification of the permutation groups G with the property that, for any non-permutation t, the semigroup generated by G and t is (von Neumann) regular. I will mention many open problems in this area.

This talk is part of the Isaac Newton Institute Seminar Series series.

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