24 citations · 93 across the 30 of their papers we have counts for
41 papers · 1 filter
The binary actions of sporadic groups
Coen del Valle, Nick Gill
An action of a group is binary if it induces the group of automorphisms of some homogeneous edge-coloured directed graph. In this paper we study the quasisimple groups with $G/…
The binary actions of alternating groups
Nick Gill, Pierre Guillot
Given a conjugacy class in a group we define a new graph, , whose vertices are elements of ; two vertices are co…
Irredundant bases for finite groups of Lie type
Nick Gill, Martin W. Liebeck
We prove that the maximum length of an irredundant base for a primitive action of a finite simple group of Lie type is bounded above by a function which is a polynomial in the rank…
A generalization of Szep's conjecture for almost simple groups
Nick Gill, Michael Giudici, Pablo Spiga
We prove a natural generalization of Szep's conjecture. Given an almost simple group with socle not isomorphic to an orthogonal group having Witt defect zero, we classify all p…
Cherlin's conjecture on finite primitive binary permutation groups
Nick Gill, Martin W. Liebeck, Pablo Spiga
A permutation group is {\it binary} if its orbits on -tuples, for any integer , can be deduced from its orbits on -tuples. Cherlin conjectured that a finite primitiv…
Statistics for acting on -sets
Nick Gill, Bianca Lodá
We study the natural action of on the set of -subsets of the set when . For this action we calculate the maximum size of a minim…