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math.GR2002
Derangements in simple and primitive groups
Jason Fulman, Robert Guralnick
We investigate the proportion of fixed point free permutations (derangements) in finite transitive permutation groups. This article is the first in a series where we prove a conjec…
math.GR2002★ 15 cited
The rational function analogue of a question of Schur and exceptionality of permutation representations
Robert M. Guralnick, Peter Müller, Jan Saxl
In 1923 Schur considered the following problem. Let f(X) be a polynomial with integer coefficients that induces a bijection on the residue fields Z/pZ for infinitely many primes p.…