QPL-group

Origin
The term was introduced by William E. Deskins in his paper On Quasinormal subgroups of finite groups, in an attempt to try to characterize what additional information could be gathered about the permutable subgroups of a group under the further condition that the intersection of permutable subgroups is permutable.

The term quasinormal subgroup is an old term for permutable subgroup.

Symbol-free definition
A finite group is said to be a QPL-group if every subgroup of it of prime power order satisfies the condition that the intersection of any two permutable subgroups in it is permutable.

Facts
Any permutable subgroup of a QPL-group is an Abelian quotient-by-core subgroup, viz its quotient by its normal core is Abelian.