IBIS primitive groups of almost simple type

TL;DR

This paper classifies a specific class of finite primitive groups called IBIS groups, focusing on those of almost simple type with a base size of at least 6, advancing understanding of their structure.

Contribution

It provides a classification of finite almost simple primitive IBIS groups with large base size, a previously unexplored category in group theory.

Findings

Identified all almost simple primitive IBIS groups with base size ≥ 6.

Established structural properties of these groups.

Extended the classification of IBIS groups in permutation group theory.

Abstract

Let $G$ be a finite permutation group on $\Omega$. An ordered sequence $(\omega_1\ldots,\omega_\ell)$ of elements of $\Omega$ is an irredundant base for $G$ if the pointwise stabilizer is trivial and no point is fixed by the stabilizer of its predecessors. The minimal cardinality of a base is said to be the base size of $G$. If all irredundant bases of $G$ have the same cardinality, $G$ is said to be an IBIS group. In this paper, we classify the finite almost simple primitive IBIS groups whose base size is at least $6$.