Pronormality in Group Theory

Abstract

A subgroup X of a group G is said to be pronormal if for each element g of G the subgroups X and X^g are conjugate in . The aim of this paper is to study pronormality and some close embedding properties, like weak normality and weak pronormality. In particular, it is proved that these properties can be countably detected, and the behaviour of groups which are rich in (generalized) pronormal subgroups is investigated.

Keywords

• pronormal subgroup
• weakly normal subgroup
• weakly pronormal subgroup