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.

External links

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

This group theory-related article is a stub. You can help Wikipedia by expanding it.

• v
• t
• e

This page was last edited on 13 August 2023, at 12:18