IBIS soluble linear groups

TL;DR

This paper classifies various classes of IBIS linear groups, including quasi-primitive soluble irreducible, nilpotent, metacyclic, and odd order groups, expanding understanding of their structure.

Contribution

It provides a comprehensive classification of quasi-primitive soluble irreducible IBIS linear groups and describes nilpotent, metacyclic, and odd order IBIS linear groups.

Findings

Classification of quasi-primitive soluble irreducible IBIS linear groups

Description of nilpotent and metacyclic IBIS linear groups

Analysis of IBIS linear groups of odd order

Abstract

Let $G$ be a finite permutation group on $\Omega.$ An ordered sequence $(\omega_1,\dots, \omega_t)$ 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. If all irredundant bases of $G$ have the same cardinality, $G$ is said to be an IBIS group. In this paper we give a classification of quasi-primitive soluble irreducible IBIS linear groups, and we also describe nilpotent and metacyclic IBIS linear groups and IBIS linear groups of odd order.