99 citations · 492 across the 111 of their papers we have counts for
11 papers · 1 filter
Strongly dense free subgroups of semisimple algebraic groups
Emmanuel Breuillard, Ben Green, Robert Guralnick +1
We show that (with one possible exception) there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroup…
Representation Growth in positive characteristic and conjugacy classes of maximal subgroups
Robert Guralnick, Michael Larsen, Pham Huu Tiep
We study the representation growth of alternating and symmetric groups in positive characteristic and restricted representation growth for the finite groups of Lie type. We show th…
A problem of Kollar and Larsen on finite linear groups and crepant resolutions
Robert Guralnick, Pham Huu Tiep
The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and o…
Simple groups admit Beauville structures
Robert Guralnick, Gunter Malle
We answer a conjecture of Bauer, Catanese and Grunewald showing that all finite simple groups other than the alternating group of degree 5 admit unmixed Beauville structures. We al…
A new solvability criterion for finite groups
Silvio Dolfi, Marcel Herzog, Cheryl E. Praeger
In 1968, John Thompson proved that a finite group is solvable if and only if every -generator subgroup of is solvable. In this paper, we prove that solvability of a fini…
On a subfactor generalization of Wall's conjecture
Robert Guralnick, Feng Xu
In this paper we discuss a conjecture on intermediate subfactors which is a generalization of Wall's conjecture from the theory of finite groups. We explore special cases of this c…
Certain subgroups of Weyl groups are split
Daniel Goldstein, Robert Guralnick
Let C be the centralizer in a finite Weyl group of an elementary abelian 2-subgroup. We show that every complex representation of C can be realized over the field of rational numbe…
Products of conjugacy classes and fixed point spaces
Robert Guralnick, Gunter Malle
We prove several results on products of conjugacy classes in finite simple groups. The first result is that there always exists a uniform generating triple. This result and other i…
Low Degree Representations of Simple Lie Groups
Robert Guralnick, Michael Larsen, Corey Manack
We give upper bounds for the number of irreducible representations of dimension at most n for a compact semisimple Lie group. In particular, we prove that there are at most n irred…
Average dimension of fixed point spaces with applications
Robert M. Guralnick, Attila Maroti
Let be a finite group, a field, and a finite dimensional -module such that has no trivial composition factor on . Then the arithmetic average dimension of th…
Frobenius subgroups of free profinite products
Robert M. Guralnick, Dan Haran
We solve an open problem of Herfort and Ribes: Profinite Frobenius groups of certain type do occur as closed subgroups of free profinite products of two profinite groups. This also…