Charles Sims

This morning I received the news that Charles Sims died on Monday.

Sims was one of the most influential figures in computational group theory, but was much more besides. His name is attached to two sporadic simple groups; the one I know best, the Higman–Sims group, was found without any recourse to computation at all. It is a subgroup of index 2 in the automorphism group of a graph on 100 vertices, constructed from the 22-point Witt design. The graph had been constructed earlier by Dale Mesner, as I described here. By coincidence it happened that the paper by Misha Klin and Andrew Woldar on this has just been published here.

Indeed, from my point of view, Higman and Sims were the two people who introduced graph theory into the study of permutation groups. I was lucky enough to be in on the ground floor, beginning my doctoral studies in 1968 (the year after the Higman–Sims group was found, though I wasn’t yet in Oxford on that memorable occasion).

Also it happened that Michael Giudici was here last week, and gave a colloquium talk about his work on extending the work of Sims and others from graphs to digraphs, and reminded me that in my thesis I extended a result of Sims on paired subconstituents of a finite transitive permutation group.

I first met Sims in the early 1970s, when he came to a miniconference on permutation groups organised by Peter Neumann. One thing that I recall is that, at Peter’s house, we were discussing perfect pitch; Charles pulled out his watch and asked me to put my ear to it and tell him the pitch of the tone. (As I recall, the mechanism cauused it to vibrate at 360 hertz.)