IBIS primitive groups of almost simple type

Abstract

Let $G$ be a finite permutation group on $\hat{I}\text{c◯}$. An ordered sequence $(\ddot{I}{‰}_1\dots ,\ddot{I}{‰}_{\ell })$ of elements of $\hat{I}\text{c◯}$ 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 $6$.

50 pages