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Automorphism orbits of groups and the Monster

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GRA - Groups, representations and applications: new perspectives

The order of an element of a group is a natural invariant of an automorphism.  In 1992, Zhang classified all finite groups such that for all integers $k$ the  automorphism group acts transitively on the set of all elements of order $k$. Such groups are called AT-groups. In this talk, I will discuss recent joint work with Alexander Bors and Cheryl Praeger that investigates two measures of how close a group is to being an AT-group. This includes a new interesting characterisation of the Monster simple group.

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

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