Conjugacy-closed Hall subgroup

Symbol-free definition
A subgroup of a group is termed a conjugacy-closed Hall subgroup if it satisfies the following conditions:


 * It is conjugacy-closed: Any two elements of the subgroup that are conjugate in the whole group are conjugate in the subgroup.
 * It is a Hall subgroup: Its order and index are relatively prime.

Stronger properties

 * Weaker than::Sylow direct factor
 * Weaker than::Sylow retract
 * Weaker than::Hall direct factor
 * Weaker than::Hall retract

Weaker properties

 * Stronger than::Conjugacy-closed subgroup
 * Stronger than::Hall subgroup