## 26 Citations

### Bases of primitive permutation groups

- Mathematics
- 2002

Let G be a permutation group on a finite set Ω of size n. A subset of Ω is said to be a base for G if its pointwise stabilizer in G is trivial. The minimal size of a base for G is denoted by b(G).…

### Primitive permutation groups of bounded orbital diameter

- Mathematics
- 2010

We give a description of infinite families of finite primitive permutation groups for which there is a uniform finite upper bound on the diameter of all orbital graphs. This is equivalent to…

### Random generation of finite and profinite groups and group enumeration

- Mathematics
- 2008

The following article appeared in Annals of Mathematics 173.2 (2011): 769-814 and may be found at http://annals.math.princeton.edu/2011/173-2/p04

### On Pyber's base size conjecture

- Mathematics
- 2013

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

- MathematicsBulletin of the London Mathematical Society
- 2019

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…

### The minimal base size for a p-solvable linear group

- Mathematics
- 2015

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…

## References

SHOWING 1-10 OF 14 REFERENCES

### The Minimal Base Size of Primitive Solvable Permutation Groups

- Mathematics
- 1996

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

- Mathematics
- 1998

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

- Mathematics
- 2001

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

- Mathematics
- 1983

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…

### Base Sizes and Regular Orbits for Coprime Affine Permutation Groups

- Mathematics
- 1998

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

- Mathematics
- 2001

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)

- Mathematics
- 2000

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

- Mathematics
- 1999

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

- Mathematics
- 1984

(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…