Semipermutable subgroup

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

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

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

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