IBIS soluble linear groups

Abstract

Let G be a finite permutation group on An ordered sequence of elements of Ω 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.