# The base size of a primitive diagonal group

```@article{Fawcett2012TheBS,
title={The base size of a primitive diagonal group},
author={Joanna B. Fawcett},
journal={Journal of Algebra},
year={2012},
volume={375},
pages={302-321}
}```
• 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
Journal of Pure and Applied Algebra
• 2022
• Mathematics
• 2013
Let \$G\$ be a permutation group on a set \$\Omega\$. A subset of \$\Omega\$ is a base for \$G\$ if its pointwise stabilizer is trivial; the base size of \$G\$ is the minimal cardinality of a base. In this
• Mathematics
J. Comb. Theory, Ser. A
• 2021
• Mathematics
Algebraic Combinatorics
• 2022
Let G be a transitive permutation group on a ﬁnite set Ω and recall that a base for G is a subset of Ω with trivial pointwise stabiliser. The base size of G , denoted b ( G ), is the minimal size of
• Mathematics
Mathematical Proceedings of the Cambridge Philosophical Society
• 2018
Abstract Let G be a permutation group on a set Ω. A subset of Ω is a base for G if its pointwise stabiliser in G is trivial. In this paper we introduce and study an associated graph Σ(G), which we
• Mathematics
• 2022
. Let G be a ﬁnite group, let H be a core-free subgroup and let b ( G, H ) denote the base size for the action of G on G/H . Let α ( G ) be the number of conjugacy classes of core-free subgroups H of

## References

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A base of a permutation group G on a set Ω is a subset B of Ω such that the pointwise stabilizer of B in G is trivial. The base size of G, denoted by b(G), is the minimal cardinality of a base. Let G
• Mathematics
• 2014
Let G be a permutation group on a set Ω. A subset B of Ω is a base for G if the pointwise stabilizer of B in G is trivial; the base size of G is the minimal cardinality of a base for G, denoted by
• Mathematics
• 2009
Let G be a permutation group on a finite set Ω. A base for G is a subset B ⊆ Ω with pointwise stabilizer in G that is trivial; we write b(G) for the smallest size of a base for G. In this paper we
• Mathematics
• 2010
Let G be a permutation group acting on a set Ω. A subset of Ω is a base for G if its pointwise stabilizer in G is trivial. We write b(G) for the minimal size of a base for G. We determine the precise
• 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
The minimal degree/~ (G) of a primitive permutat ion group G of degree n on a set ~, that is, the smallest number of points moved by any non-identity element of G, has been the subject of
Let G be a finite almost simple classical group and let Ω be a faithful primitive non‐standard G‐set. A subset of Ω is a base for G if its pointwise stabilizer in G is trivial. Let b(G) be the
• 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
• 1984
Let G be a permutation group on a finite set f2 of size n. Then G acts naturally on the set P (f2) of all subsets of f2. In this note we shall show that if G is primitive on f2 and A, \$ G then in all