Some Classes of Finite Supersoluble Groups

Abstract

In this survey we study the relation between the class of groups in which Sylow permutability is a transitive relation (the PST-groups) and the class of groups in which every subgroup possesses supergroups of all possible indices, the so-called -groups. The parellelism between these classes in the soluble universe and the interest of the local study of PST-groups motivates a local study of -groups.

A group  factorised as a product of two subgroups  and  is said to be a mutually permutable product whenever   permutes with every subgroup of  and  permutes with every subgroup of . We present some results concerning mutually permutable products of groups in the orbit of the above classes.