## 27 Citations

### 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…

### On base sizes for primitive groups of product type

- MathematicsJournal of Pure and Applied Algebra
- 2022

### On base sizes for algebraic groups

- 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…

### On the Saxl graphs of primitive groups with soluble stabilisers

- MathematicsAlgebraic 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…

### On the Saxl graph of a permutation group

- MathematicsMathematical 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…

### Strongly base-two groups

- 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

SHOWING 1-10 OF 38 REFERENCES

### On base sizes for symmetric groups

- Mathematics
- 2011

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…

### Base sizes for S-actions of finite classical groups

- 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…

### Base sizes for simple groups and a conjecture of Cameron

- 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…

### Base sizes for sporadic simple groups

- 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…

### 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…

### On minimal degrees and base sizes of primitive permutation groups

- Mathematics
- 1984

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…

### On base sizes for actions of finite classical groups

- Mathematics
- 2007

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…

### 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).…

### On groups with no regular orbits on the set of subsets

- 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…