99 citations · 492 across the 111 of their papers we have counts for
7 papers · 2 filters
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…
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…
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…
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…