Finite groups with given systems of propermutable subgroups

Abstract

Let H be a subgroup of a finite group G. Then we say that H is propermutable in G provided G has a subgroup B such that G = NG(H)B and H permutes with all subgroups of B. In this paper, we present new properties of propermutable subgroups. Also we provide new information on the structure of a group with propermutable Sylow (Hall, maximal) subgroups and a group G = AB with propermutable subgroups A and B.