Bases of primitive linear groups

@article{Liebeck2002BasesOP,
  title={Bases of primitive linear groups},
  author={Martin W. Liebeck and Aner Shalev},
  journal={Journal of Algebra},
  year={2002},
  volume={252},
  pages={95-113}
}
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26 Citations
Highly Influential Citations
3
Background Citations
12
Methods Citations
3

26 Citations

Bases of primitive linear groups II

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Let G be a permutation group on a finite set Ω. A subset of Ω is a base for G if its pointwise stabilizer in G is trivial. The base size of G, denoted b(G), is the smallest size of a base. A…

An improved diameter bound for finite simple groups of Lie type

For a finite group G , let diam (G) denote the maximum diameter of a connected Cayley graph of G . A well‐known conjecture of Babai states that diam (G) is bounded by (log2|G|)O(1) in case G is a…

A proof of Pyber's base size conjecture

The minimal base size for a p-solvable linear group

Let $V$ be a finite vector space over a finite field of order $q$ and of characteristic $p$. Let $G\leq GL(V)$ be a $p$-solvable completely reducible linear group. Then there exists a base for $G$ on…

Bases of twisted wreath products

The base size of a primitive diagonal group

References

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The Minimal Base Size of Primitive Solvable Permutation Groups

A base of a permutation group G is a sequence B of points from the permutation domain such that only the identity of G fixes B pointwise. Answering a question of Pyber, we prove that all primitive…

Bases for Primitive Permutation Groups and a Conjecture of Babai

Abstract A base of a permutation group G is a sequence B of points from the permutation domain such that only the identity of G fixes B pointwise. We show that primitive permutation groups with no…

Small Degree Representations of Finite Chevalley Groups in Defining Characteristic

The author has determined, for all simple simply connected reductive linear algebraic groups defined over a finite field, all the irreducible representations in their defining characteristic of…

The local structure of finite groups of characteristic 2 type

Part I: Properties of $K$-groups and Preliminary Lemmas: Introduction Decorations of the known simple groups Local subgroups of the known simple groups Balance and signalizers Generational properties…

Finite Group Theory: Index

Base Sizes and Regular Orbits for Coprime Affine Permutation Groups

Let G be a permutation group on a finite set Ω. A sequence B=(ω1, …, ωb) of points in Ω is called a base if its pointwise stabilizer in G is the identity. Bases are of fundamental importance in…

Diameters of finite simple groups: sharp bounds and applications

Let G be a finite simple group and let S be a normal subset of G. We determine the diameter of the Cayley graph r(G, S) associated with G and S, up to a multiplicative constant. Many applications…

Intersections of Matrix Algebras and Permutation Representations of PSL(n, q)

Abstract If G is a group, H a subgroup of G , and Ω a transitive G -set we ask under what conditions one can guarantee that H has a regular orbit ( = of size | H |) on Ω. Here we prove that if PSL (…

Simple groups, permutation groups, and probability

In recent years probabilistic methods have proved useful in the solution of several problems concerning finite groups, mainly involving simple groups and permutation groups. In some cases the…

On the maximal subgroups of the finite classical groups

(1.1) Definition Let 1 6= G be a group. A subgroup M of G is said to be maximal if M 6= G and there exists no subgroup H such that M < H < G. IfG is finite, by order reasons every subgroupH 6= G is…