Completely simple semigroup with basis property

Abstract

An inverse semigroup (group) S is called an inverse semigroup (group) with basis property, if each two minimal (irreducible) generating sets (with respect to inclusion) of an arbitrary subsemigroup (group) H of S is equivalent (i.e. they have the same cardinality).

It is proved that every completely simple semigroup with basis property is either group with basis property or its sandwich matrix has at most two rows or two column and its maximal subgroup is either trivial group or a primary cyclic group.