Sylow subgroup of normal subgroup

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


 * 1) It is a Sylow subgroup of a normal subgroup of the whole group.
 * 2) It is the intersection of a normal subgroup of the whole group with a Sylow subgroup of the whole group.
 * 3) It is a Sylow subgroup inside its normal closure.

Stronger properties

 * Weaker than::Sylow subgroup

Weaker properties

 * Stronger than::Intermediately isomorph-conjugate subgroup of normal subgroup
 * Stronger than::Pronormal subgroup:
 * Stronger than::Normal subgroup of Sylow subgroup
 * Stronger than::Sylow subgroup of permutable subgroup