99 citations · 492 across the 111 of their papers we have counts for
7 papers · 1 filter
Adequate Subgroups II
Robert Guralnick
The notion of adequate subgroups was introduced by Jack Thorne. It is a weakening of the notion of big subgroup used by Wiles and Taylor in proving automorphy lifting theorems for…
Lifting in Frattini Covers and A Characterization of Finite Solvable Groups
Robert Guralnick, Pham Huu Tiep
We prove a lifting theorem for odd Frattini covers of finite groups. Using this, we characterize solvable groups and more generally p-solvable groups in terms of containing a tripl…
Characteristic Polynomials and Fixed Spaces of Semisimple Elements
Robert Guralnick, Gunter Malle
Answering a question of Frank Calegari, we extend some of our earlier results on dimension of fixed point spaces of elements in irreducible linear groups. We consider characteristi…
Coprime subdegrees for primitive permutation groups and completely reducible linear groups
Silvio Dolfi, Robert Guralnick, Cheryl Praeger +1
In this paper we answer a question of Gabriel Navarro about orbit sizes of a finite linear group H acting completely reducibly on a vector space V: if the orbits containing the vec…
Adequate subgroups
Robert Guralnick, Florian Herzig, Richard Taylor +1
We study adequate subgroups of over a finite field. This notion is useful in the study of automorphy lifting theorems. In particular, we give a sufficient condition for a su…
A new solvability criterion for finite groups
Silvio Dolfi, Robert Guralnick, Marcel Herzog +1
In 1968, John Thompson proved that a finite group G is solvable if and only if every 2-generator subgroup of G is solvable. In this paper, we prove that solvability of a finite gro…
The Automorphism Groups of a Family of Maximal Curves
Robert Guralnick, Beth Malmskog, Rachel Pries
The Hasse Weil bound restricts the number of points of a curve which are defined over a finite field; if the number of points meets this bound, the curve is called maximal. Giuliet…