Normal Sylow subgroup

Definition
A subgroup of a defining ingredient::finite group is termed a normal Sylow subgroup if it satisfies the following equivalent conditions:


 * It is a Sylow subgroup, and is normal in the whole group.
 * It is a Sylow subgroup, and is subnormal in the whole group.
 * It is a Sylow subgroup, and is characteristic in the whole group.
 * It is a Sylow subgroup, and is fully characteristic in the whole group.

Stronger properties

 * Weaker than::Sylow direct factor

Weaker properties

 * Stronger than::Nilpotent normal subgroup
 * Stronger than::Nilpotent characteristic subgroup
 * Stronger than::Normal Hall subgroup
 * Stronger than::Complemented normal subgroup
 * Stronger than::Fully characteristic subgroup
 * Stronger than::Characteristic subgroup
 * Stronger than::Intermediately characteristic subgroup
 * Stronger than::Isomorph-free subgroup
 * Stronger than::Intermediately fully characteristic subgroup
 * Stronger than::Image-closed characteristic subgroup
 * Stronger than::Image-closed fully characteristic subgroup
 * Stronger than::Normal subgroup