Conjugate-permutable subgroup

In group theory, a **conjugate-permutable subgroup** is a specific type of subgroup that has a particular property related to conjugation. A subgroup \( H \) of a group \( G \) is said to be conjugate-permutable if for every element \( g \in G \), the following condition holds: \[ H^g = gHg^{-1} \text{ satisfies } H^g \cap H \neq \emptyset.