## 10 Citations

### Saxl graphs of primitive affine groups with sporadic point stabilisers

- Mathematics
- 2021

Let G be a permutation group on a set Ω. A base for G is a subset of Ω whose pointwise stabiliser is trivial, and the base size of G is the minimal cardinality of a base. If G has base size 2, then…

### 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…

### 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…

### Non-solvable groups whose character degree graph has a cut-vertex. II

- MathematicsAnnali di Matematica Pura ed Applicata (1923 -)
- 2023

. Let G be a ﬁnite group, and let cd( G ) denote the set of degrees of the irreducible complex characters of G . Deﬁne then the character degree graph ∆( G ) as the (simple undirected) graph whose…

### 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…

### On the Classification of Extremely Primitive Affine Groups

- MathematicsIsrael Journal of Mathematics
- 2022

Let G be a finite non-regular primitive permutation group on a set Ω with point stabiliser Gα. Then G is said to be extremely primitive if Gα acts primitively on each of its orbits in Ω \ {α}, which…

### Base sizes for finite groups of Lie type in cross-characteristic

- Mathematics
- 2019

Let $G \leq \mathrm{GL}(V)$ be a group with a unique subnormal quasisimple subgroup $E(G)$ that acts absolutely irreducibly on $V$. A base for $G$ acting on $V$ is a set of vectors with trivial…

## References

SHOWING 1-10 OF 32 REFERENCES

### Regular Orbits of Linear Groups with an Application to the k(GV)-Problem, 1

- Mathematics
- 2000

Abstract Let p be a prime, G a finite group of order coprime to p, and V a faithful F pG-module. Suppose G has a normal quasi-simple irreducible subgroup H. We show that either G has a regular orbit…

### 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 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…

### 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…

### Computing Projective Indecomposable Modules and Higher Cohomology Groups

- MathematicsExp. Math.
- 2013

We describe the theory and implementation in Magma of algorithms to compute the projective indecomposable KG-modules for finite groups G and finite fields K. We describe also how they may be used…

### Finite Simple Groups: An Introduction to Their Classification

- Mathematics
- 1982

In February 1981, the classification of the finite simple groups (Dl)* was completed,t. * representing one of the most remarkable achievements in the history or mathematics. Involving the combined…