99 citations · 492 across the 111 of their papers we have counts for
9 papers · 2 filters
Variations on the Baer--Suzuki Theorem
Robert Guralnick, Gunter Malle
The Baer--Suzuki theorem says that if is a prime, is a -element in a finite group and is a -group for all , then the normal clos…
On base sizes for algebraic groups
Timothy Burness, Robert Guralnick, Jan Saxl
Let be a permutation group on a set . A subset of is a base for if its pointwise stabilizer is trivial; the base size of is the minimal cardinality of a base. In…
Simple groups stabilizing polynomials
Skip Garibaldi, Robert Guralnick
We study the problem of determining, for a polynomial function on a vector space , the linear transformations of such that . In case is invariant under…
Expansion in finite simple groups of Lie type
Emmanuel Breuillard, Ben Green, Robert Guralnick +1
We show that random Cayley graphs of finite simple (or semisimple) groups of Lie type of fixed rank are expanders. The proofs are based on the Bourgain-Gamburd method and on the ma…
On the non-coprime k(GV) problem
Robert M. Guralnick, Attila Maroti
Let V be a finite faithful completely reducible FG-module for a finite field F and a finite group G. In various cases explicit linear bounds in |V| are given for the numbers of con…
Derangements in Subspace Actions of Finite Classical Groups
Jason Fulman, Robert Guralnick
This is the third in a series of papers in which we prove a conjecture of Boston and Shalev that the proportion of derangements (fixed point free elements) is bounded away from zer…
Products and commutators of classes in algebraic groups
Robert Guralnick, Gunter Malle
We classify pairs of conjugacy classes in almost simple algebraic groups whose product consists of finitely many classes. This leads to several interesting families of examples whi…
Bass units as free factors in integral group rings of simple groups
Jairo Z. Gonçalves, Robert M. Guralnick, Ángel del Río
Let be a finite group, a Bass unit based on an element of of prime order, and assume that has infinite order modulo the center of the units of the integral grou…
Effective Results on the Waring Problem for Finite Simple Groups
Robert M. Guralnick, Pham Huu Tiep
Let G be a finite quasisimple group of Lie type. We show that there are regular semisimple elements x,y in G, x of prime order, and |y| is divisible by at most two primes, such tha…