Source: wikibot/maximal-compact-subgroup
= Maximal compact subgroup
{wiki=Maximal_compact_subgroup}
In the context of Lie groups and algebraic groups, a **maximal compact subgroup** is a specific type of subgroup that has particular significance in the study of group structures. \#\#\# Definition: A **maximal compact subgroup** of a Lie group \\( G \\) is a compact subgroup \\( K \\) of \\( G \\) such that there is no other compact subgroup \\( H \\) of \\( G \\) that properly contains \\( K \\) (i.e.