Derangements for transitive group actions
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)usc.edu
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