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Simple binary permutation groups

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GRA2 - Groups, representations and applications: new perspectives

The notion of a “binary” permutation group is due to the model theorist, Gregory Cherlin. Roughly speaking, if G is a permutation group on a set X, then we call G “binary” if the orbits of G on Xn, for any positive integer n, can be determined from the orbits of G on X2. This notion has close connections to the concept of a “homogeneous relational structure”. Thanks to the work of various authors we have a full classification of the finite binary PRIMITIVE permutation groups. In this talk I will discuss recent work aimed at extending this classification to imprimitive permutation groups and even intransitive permutation groups. My main focus will be on the situation where the permutation group is simple.

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

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