43 citations · 213 across the 16 of their papers we have counts for
11 papers · 1 filter
Beauville surfaces and probabilistic group theory
Shelly Garion
A Beauville surface is a complex algebraic surface that can be presented as a quotient of a product of two curves by a suitable action of a finite group. Bauer, Catanese and Grunew…
Expansion of conjugacy classes in PSL(2,q)
Shelly Garion
For any conjugacy class C in G=PSL(2,q) we compute C^2 and discuss whether C contains a triple of elements whose product is 1 which generate G. Moreover, we determine which element…
Surjectivity and equidistribution of the word x^ay^b on PSL(2,q) and SL(2,q)
Tatiana Bandman, Shelly Garion
We determine the positive integers a,b and the prime powers q for which the word map w(x,y)=x^ay^b is surjective on the group PSL(2,q) (and SL(2,q)). We moreover show that this map…
On the Surjectivity of Engel Words on PSL(2,q)
Tatiana Bandman, Shelly Garion, Fritz Grunewald
We investigate the surjectivity of the word map defined by the n-th Engel word on the groups PSL(2,q) and SL(2,q). For SL(2,q), we show that this map is surjective onto the subset…
Highly Transitive Actions of Out(Fn)
Shelly Garion, Yair Glasner
An action of a group on a set is called k-transitive if it is transitive on ordered k-tuples and highly transitive if it is k-transitive for every k. We show that for n>3 the group…
Beauville surfaces and finite simple groups
Shelly Garion, Michael Larsen, Alexander Lubotzky
A Beauville surface is a rigid complex surface of the form (C1 x C2)/G, where C1 and C2 are non-singular, projective, higher genus curves, and G is a finite group acting freely on…
On Beauville Structures for PSL(2,q)
Shelly Garion
We characterize Beauville surfaces of unmixed type with group either PSL(2,p^e) or PGL(2,p^e), thus extending previous results of Bauer, Catanese and Grunewald, Fuertes and Jones,…
New Beauville surfaces and finite simple groups
Shelly Garion, Matteo Penegini
In this paper we construct new Beauville surfaces with group either $\PSL(2,p^e)$, or belonging to some other families of finite simple groups of Lie type of low Lie rank, or an al…
Connectivity of the Product Replacement Algorithm Graph of PSL(2,q)
Shelly Garion
The product replacement algorithm is a practical algorithm to construct random elements of a finite group G. It can be described as a random walk on a graph whose vertices are the…
Connectivity of the Product Replacement Graph of Simple Groups of Bounded Lie Rank
Nir Avni, Shelly Garion
The Product Replacement Algorithm is a practical algorithm for generating random elements of a finite group. The algorithm can be described as a random walk on a graph whose vertic…
Commutator maps, measure preservation, and T-systems
Shelly Garion, Aner Shalev
Let G be a finite simple group. We show that the commutator map is almost equidistributed as the order of G goes to infinity. This somewhat surprising result…