Add to ORKGAbstract. Let V be a finite vector space over a finite field of order q and of characteristic p. Let G ≤ GL(V) be a p-solvable completely reducible linear group. Then there exists a base for G on V of size at most 2 unless q ≤ 4 in which case there exists a base of size at most 3. The first statement extends a recent result of Halasi and Podoski and the second statement generalizes a theorem of Seress. An extension of a theorem of Pálfy and Wolf is also given. Dedicated to the memory of Ákos Seress. 1
Let G be a permutation group acting on a set Ω. A subset of Ω is a base for G if its pointwise stabi...
AbstractWe present conditions on the structure and degree n of a finite irreducible complex linear g...
Building on earlier papers of several authors, we establish that there exists a universal constan...
AbstractLet V be a finite vector space and G⩽GL(V) a linear group. A base of G is a set of vectors w...
A generating set for a finite group G is minimal if no proper subset generates G, and m(G) denotes t...
AbstractWe present conditions on the structure and degree n of a finite irreducible complex linear g...
Let V be a vector space of dimension d over Fq, a finite field of q elements, and let G≤GL (V)∼=GLd(...
Let G be a finite almost simple classical group and let Ω be a faithful primitive non-standard G-set...
AbstractA base B for a finite permutation group G acting on a set Ω is a subset of Ω with the proper...
AbstractLet q be a power of some prime number p. Let G be a connected reductive group defined over t...
A base for a permutation group G ≤ Sym(Ω) is a subset B ⊆ Ω such that the pointwise stabiliser GB of...
We show that the minimal base size $b(G)$ of a finite primitive permutation group $G$ of degree $n$ ...
We denote the smallest size of a generating set of a group G by . We prove that for irreducible sub...
AbstractLet q be a power of some prime number p. Let G be a connected reductive group defined over t...
Let $k $ be a field of characteristic $\ell>0 $. In this note, we consider the $\ell$-modular rep...
Let G be a permutation group acting on a set Ω. A subset of Ω is a base for G if its pointwise stabi...
AbstractWe present conditions on the structure and degree n of a finite irreducible complex linear g...
Building on earlier papers of several authors, we establish that there exists a universal constan...
AbstractLet V be a finite vector space and G⩽GL(V) a linear group. A base of G is a set of vectors w...
A generating set for a finite group G is minimal if no proper subset generates G, and m(G) denotes t...
AbstractWe present conditions on the structure and degree n of a finite irreducible complex linear g...
Let V be a vector space of dimension d over Fq, a finite field of q elements, and let G≤GL (V)∼=GLd(...
Let G be a finite almost simple classical group and let Ω be a faithful primitive non-standard G-set...
AbstractA base B for a finite permutation group G acting on a set Ω is a subset of Ω with the proper...
AbstractLet q be a power of some prime number p. Let G be a connected reductive group defined over t...
A base for a permutation group G ≤ Sym(Ω) is a subset B ⊆ Ω such that the pointwise stabiliser GB of...
We show that the minimal base size $b(G)$ of a finite primitive permutation group $G$ of degree $n$ ...
We denote the smallest size of a generating set of a group G by . We prove that for irreducible sub...
AbstractLet q be a power of some prime number p. Let G be a connected reductive group defined over t...
Let $k $ be a field of characteristic $\ell>0 $. In this note, we consider the $\ell$-modular rep...
Let G be a permutation group acting on a set Ω. A subset of Ω is a base for G if its pointwise stabi...
AbstractWe present conditions on the structure and degree n of a finite irreducible complex linear g...
Building on earlier papers of several authors, we establish that there exists a universal constan...