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Automorphism orbits of groups and the Monster

Presented by: 
Michael Giudici
Date: 
Thursday 23rd January 2020 - 16:00 to 17:00
Venue: 
INI Seminar Room 2
Abstract: 
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.




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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons