FINITE GROUPS WITH HEREDITARILY G-PERMUTABLE SCHMIDT SUBGROUPS

Abstract A subgroup A of a group G is said to be hereditarily G -permutable with a subgroup B of G , if $AB^x = B^xA$ for some element $x \in \langle A, B \rangle $ . A subgroup A of a group G is said to be hereditarily G -permutable in G if A is hereditarily G -permutable with every subgroup of G . In this paper, we investigate the structure of a finite group G with all its Schmidt subgroups hereditarily G -permutable.