Semipermutable subgroup

In mathematics, in algebra, in the realm of group theory, a subgroup [math]\displaystyle{ H }[/math] of a finite group [math]\displaystyle{ G }[/math] is said to be semipermutable if [math]\displaystyle{ H }[/math] commutes with every subgroup [math]\displaystyle{ K }[/math] whose order is relatively prime to that of [math]\displaystyle{ H }[/math]. Clearly, every permutable subgroup of a finite group is semipermutable. The converse, however, is not necessarily true.

External links

• The Influence of semipermutable subgroups on the structure of finite groups