Sylow subgroup of permutable subgroup

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


 * It can be expressed as a Sylow subgroup of a permutable subgroup of the whole group.
 * It can be expressed as the intersection of a Sylow subgroup of the whole group and a permutable subgroup of the whole group.

Stronger properties

 * Weaker than::Sylow subgroup
 * Weaker than::Sylow subgroup of normal subgroup