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
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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…