Dedicated to the memory of Jan Saxl Let be a finite primitive permutation group on a set with
nontrivial point stabilizer. We say that is extremely primitive if acts primitively on each of its …

We study the base sizes of finite quasiprimitive permutation groups of twisted wreath type,
which are precisely the finite permutation groups with a unique minimal normal subgroup …

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 …

Let V be a finite-dimensional vector space over a finite field, and suppose G≤ Γ L (V) is a
group with a unique subnormal quasisimple subgroup E (G) that is absolutely irreducible on …

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 Δ (G) as the (simple undirected) …

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 …

A base for a finite permutation group $ G\le\mathrm {Sym}(\Omega) $ is a subset of $\Omega
$ with trivial pointwise stabiliser in $ G $, and the base size of $ G $ is the smallest size of a …

On the degrees of irreducible characters fixed by some field automorphism in finite groups -
Grittini - 2025 - Bulletin of the London Mathematical Society - Wiley Online Library Skip to Article …

Abstract Let G⩽ Sym (Ω) be a finite permutation group and recall that the base size of G is
the minimal size of a subset of Ω with trivial pointwise stabiliser. There is an extensive …

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