Decomposizione ed s-m rappresentazione di gruppi finiti

This paper is a survey of a few previous works of the authors with other new results. We introduce a special decomposition of a finite group [semigroup] and determine its main properties. From such a decomposition one can construct, for a special class of finite groups, a set-matrix representation. The group D_4 has such a representation. Several theorems were already obtained on groups with s-m representation.