Let G be a finite permutation group on Ω. An ordered sequence of elements Ω, (ω1,…,ωt), is an irredundant base for if the pointwise stabilizer G(ω1,…,ωt) trivial and no point fixed by its predecessors. If all bases have same size we say that IBIS group. In this paper show primitive IBIS, then it must almost simple, affine-type, or diagonal type. Moreover prove diagonal-type groups only isomorph...

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus, every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fai...