Source: wikibot/semipermutable-subgroup
= Semipermutable subgroup
{wiki=Semipermutable_subgroup}
A semipermutable subgroup is a concept in the field of group theory, particularly in the study of group extensions and solvable groups. A subgroup \\( H \\) of a group \\( G \\) is called **semipermutable** if for every normal subgroup \\( N \\) of \\( G \\) such that \\( N \\) is a subset of \\( H \\), the subgroup \\( H \\) permutes with \\( N \\) in \\( G \\).