Derangements for transitive group actions

Robert Guralnick


May 16,
refreshments at 3:45pm


It is a classical result dating back to Jordan that any finite transitive permutation group contains derangements (permutations without fixed points). Rather remarkably, it was not until 1993 that it was shown that if the degree is n > 1, then the proportion of derangements is at least 1/n. We will discuss variations on this theme in the context of algebraic groups and finite simple and almost simple groups. In particular, we will discuss our recent result with Fulman about derangements in simple groups. Also, we will consider the problem of finding derangements in a given coset of a normal subgroup and applications to covers of curves over finite fields.

Speaker's Contact Info: guralnic(at-sign)

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)

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