Hall direct factor

Definition
A subgroup of a finite group is termed a Hall direct factor if it satisfies the following equivalent conditions:


 * 1) It is a Hall subgroup and is also a direct factor.
 * 2) It is a normal Hall subgroup and possesses a normal complement, i.e., is a retract.
 * 3) It is a Hall subgroup and is also a central factor of the whole group.

Stronger properties

 * Weaker than::Sylow direct factor

Weaker properties

 * Stronger than::Normal Hall subgroup
 * Stronger than::Fully characteristic subgroup
 * Stronger than::Fully characteristic direct factor
 * Stronger than::Direct factor
 * Stronger than::Central factor
 * Stronger than::Conjugacy-closed normal subgroup
 * Stronger than::Conjugacy-closed Hall subgroup