Primitive almost simple IBIS groups with sporadic socle

TL;DR

This paper classifies primitive IBIS groups that are almost simple with sporadic socle, advancing understanding of their structure and properties in permutation group theory.

Contribution

It provides a classification of primitive IBIS groups with sporadic socle that are almost simple, filling a gap in the existing group theory literature.

Findings

Identified all primitive IBIS groups with sporadic socle that are almost simple.

Established criteria for IBIS property in these groups.

Enhanced the understanding of the structure of primitive permutation groups.

Abstract

An irredundant base $B$ for a permutation group $G\leq \mathrm{Sym}(\Omega)$ is an ordered subset of $\Omega$ with trivial stabiliser such that no base point is fixed by the stabiliser of its predecessors. Groups whose irredundant bases all have the same size are termed Irredundant Bases of Invariant Size (IBIS) groups, and were introduced by Cameron and Fon-Der-Flaass. In this paper, we contribute to the classification of primitive IBIS groups by classifying those that are almost simple with sporadic socle.