SEMINAR: Groups and Combinatorics Seminar: Classical groups, derangements and primes

Time and place: 15:00 Friday 27 November in MLR1.

Speaker: Michael Giudici (University of Western Australia)

Title: Classical groups, derangements and primes

Abstract: An elementary result of Jordan shows that every finite transitive group of degree at least two contains a derangement, that is an element that fixes no points. It was later shown by Fein, Kantor and Schacher that there is actually a derangement of prime power order. There is not always one of prime order but in the primitive group case all primitive groups without a derangement of prime order are known. When Tim Burness came to visit in 2008, we started a program of trying to determine for a given primitive group, for which primes p there is a derangement of order p. A large part of these investigations will be appearing in our very soon to be released booked of the same title. In this talk I will give a brief outline of some of the contents. It will be a sequel to my talk in this series on the 8th of September 2009. No knowledge of that talk will be required.