Editing Compact group (section)

==Further examples==

Amongst groups that are not Lie groups, and so do not carry the structure of a [[manifold]], examples are the additive group ''Z''<sub>''p''</sub> of [[p-adic integer]]s, and constructions from it. In fact any [[profinite group]] is a compact group. This means that [[Galois group]]s are compact groups, a basic fact for the theory of [[algebraic extension]]s in the case of infinite degree.

[[Pontryagin duality]] provides a large supply of examples of compact commutative groups. These are in duality with abelian [[discrete group]]s.