[[Group theory MOC]]
# Compact group

A **compact group** $G$ is a [[topological group]] which is [[compact space|compact]] as a topological space. #m/def/group 

## Properties

- [[A compact group is unimodular]]

## Examples

- If $G$ is a [[Discrete group]] then it is compact iff it is a [[Finite group]]. Hence all finite groups may be identified as compact groups.
- [[Compact Lie group]]

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