Editing Maximal compact subgroup (section)

{{Short description|Concept in topology}}
In [[mathematics]], a '''maximal compact subgroup''' ''K'' of a [[topological group]] ''G'' is a [[subgroup]] ''K'' that is a [[compact space]], in the [[subspace topology]], and [[maximal element|maximal]] amongst such subgroups.

Maximal compact subgroups play an important role in the classification of [[Lie group]]s and especially semi-simple Lie groups. Maximal compact subgroups of Lie groups are ''not'' in general unique, but are unique up to [[Conjugacy class#Conjugacy of subgroups and general subsets|conjugation]] – they are [[essentially unique]].