Semipermutable subgroup

In mathematics, in algebra, in the realm of group theory, a subgroup $$H$$ of a finite group $$G$$ is said to be semipermutable if $$H$$ commutes with every subgroup $$K$$ whose order is relatively prime to that of $$H$$.

Clearly, every permutable subgroup of a finite group is semipermutable. The converse, however, is not necessarily true.