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Presentations of Finite Simple Groups: Profinite and Cohomological Approaches
Robert Guralnick, William M. Kantor, Martin Kassabov +1
We prove the following three closely related results. The first is that every finite simple group has a profinite presentation with 2 generators and at most 18 relations. The secon…
Oort groups and lifting problems
Ted Chinburg, Robert Guralnick, David Harbater
Let k be an algebraically closed field of positive characteristic p. We consider which finite groups G have the property that every faithful action of G on a connected smooth proje…
On fixed points of permutations
Persi Diaconis, Jason Fulman, Robert Guralnick
The number of fixed points of a random permutation of 1,2,...,n has a limiting Poisson distribution. We seek a generalization, looking at other actions of the symmetric group. Rest…
A new family of exceptional polynomials in characteristic two
Robert M. Guralnick, Joel E. Rosenberg, Michael E. Zieve
We produce a new family of polynomials f(x) over fields K of characteristic 2 which are exceptional, in the sense that f(x)-f(y) has no absolutely irreducible factors in K[x,y] bes…
Polynomials with PSL(2) monodromy
Robert M. Guralnick, Michael E. Zieve
Let K be a field of characteristic p>0, and let q be a power of p. We determine all polynomials f in K[t]\K[t^p] of degree q(q-1)/2 such that the Galois group of f(t)-u over K(u) h…
Frobenius-Schur Indicators for Subgroups and the Drinfel'd Double of Weyl Groups
Robert Guralnick, Susan Montgomery
If G is a finite group and k is a field, there is a natural construction of a Hopf algebra over k associated to G, the Drinfel'd double D(G). We prove that if G is any finite real…