Sylow direct factor

Symbol-free definition
A subgroup of a finite group is termed a Sylow direct factor if it satisfies the following equivalent conditions:


 * 1) It is a Sylow subgroup and is also a direct factor of the group.
 * 2) It is a normal Sylow subgroup and possesses a normal p-complement, i.e., it is a retract of the group.
 * 3) It is a Sylow subgroup and is also a central factor of the whole group.
 * 4) It is a Sylow subgroup and is also a conjugacy-closed normal subgroup of the whole group.

Weaker properties

 * Stronger than::Normal Sylow subgroup
 * Stronger than::Hall direct factor
 * Stronger than::Normal Hall subgroup
 * Stronger than::Fully characteristic subgroup
 * Stronger than::Characteristic subgroup
 * Stronger than::Direct factor
 * Stronger than::Central factor