# 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}
}
• Published 1 June 2002
• Mathematics
• Journal of Algebra
26 Citations
• 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).
• 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
• 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
• 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
• Mathematics
Bulletin 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
• 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