"A generalization to Sylow permutability of pronormal subgroups of finite groups"

In this note, we present a new subgroup embedding property that can be considered as an analogue of pronormality in the scope of permutability and Sylow permutability in finite groups. We prove that finite PST-groups, or groups in which Sylow permutability is a transitive relation, can be characterized in terms of this property, in a similar way as T-groups, or groups in which normality is transitive, can be characterized in terms of pronormality. Here a subgroup H of a group G is said to be pronormal when given g ∈ G, there exists x ∈ such that H^g = H^x.