Results 21 to 30 of about 331 (55)

Linear Approximate Groups

, 2010
This is an informal announcement of results to be described and proved in detail in a paper to appear. We give various results on the structure of approximate subgroups in linear groups such as $\SL_n(k)$.
Breuillard, Emmanuel, Green, Ben, Tao, Terence   +2 more
core   +1 more source

Moments, Exponential Sums, and Monodromy Groups

Forum of Mathematics, Sigma
We determine the geometric monodromy groups attached to various families, both one-parameter and multi-parameter, of exponential sums over finite fields, or, more precisely, the geometric monodromy groups of the $\ell $ -adic local systems on ...
Nicholas M. Katz, Pham Huu Tiep
doaj   +1 more source

The simple classical groups of dimension less than 6 which are (2,3)-generated

, 2015
In this paper we determine the classical simple groups of dimension r=3,5 which are (2,3)-generated (the cases r = 2, 4 are known). If r = 3, they are PSL_3(q), q 4, and PSU_3(q^2), q^2 9, 25. If r = 5 they are PSL_5(q), for all q, and PSU_5(q^2), q^2 >
Bellani, M. C. Tamburini, Pellegrini, M. A.   +1 more
core   +1 more source

The Divisibility Graph of finite groups of Lie Type

, 2016
The Divisibility Graph of a finite group $G$ has vertex set the set of conjugacy class lengths of non-central elements in $G$ and two vertices are connected by an edge if one divides the other.
Abdolghafourian, Adeleh, Iranmanesh, Mohammad A., Niemeyer, Alice C.   +2 more
core   +1 more source

On the K-theoretic fundamental classes of Deligne-Lusztig varieties

, 2020
In this paper we express the class of the structure sheaves of the closures of Deligne--Lusztig varieties as explicit double Grothendieck polynomials in the first Chern classes of appropriate line bundles on the ambient flag variety.
Hudson, Thomas, Peters, Dennis
core  

The $(2,3)$-generation of the finite unitary groups

, 2019
In this paper we prove that the unitary groups $SU_n(q^2)$ are $(2,3)$-generated for any prime power $q$ and any integer $n\geq 8$. By previous results this implies that, if $n\geq 3$, the groups $SU_n(q^2)$ and $PSU_n(q^2)$ are $(2,3)$-generated, except
Bellani, M. C. Tamburini, Pellegrini, M. A.   +1 more
core   +1 more source

The ElGamal cryptosystem over circulant matrices [PDF]

, 2011
In this paper we study extensively the discrete logarithm problem in the group of non-singular circulant matrices. The emphasis of this study was to find the exact parameters for the group of circulant matrices for a secure implementation.
Mahalanobis, Ayan
core   +3 more sources

The Ring of Support-Classes of $\mathrm{SL}\_2(\mathbb F\_q)$

, 2015
We introduce and study a subring $\mathcal{SC}$ of $\mathbb Z[\mathrm{SL}\_2(\mathbb F\_q)]$ obtained by summing elements of $\mathrm{SL}\_2(\mathbb F\_q)$ according to their support.
Bacher, Roland
core  

The (2,3)-generation of the classical simple groups of dimension 6 and 7

, 2015
In this paper we prove that the finite simple groups $PSp_6(q)$, $\Omega_7(q)$ and $PSU_7(q^2)$ are (2,3)-generated for all q. In particular, this result completes the classification of the (2,3)-generated finite classical simple groups up to dimension ...
Pellegrini, Marco Antonio
core  

Intersections of conjugate solvable subgroups in classical groups of Lie type

, 2017
In this paper we obtain a partial solution to Problem 17.41 from "Kourovka notebook": if $S$ is a solvable subgroup of a finite group $G$ with trivial solvable radical, do there exist five conjugate of $S$ with trivial intersection. We consider the case,
Baykalov, Anton
core