Further Examples
Amongst groups that are not Lie groups, and so do not carry the structure of a manifold, examples are the additive group Zp of p-adic integers, and constructions from it. In fact any profinite group is a compact group. This means that Galois groups are compact groups, a basic fact for the theory of algebraic extensions 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 groups.
Read more about this topic: Compact Group
Famous quotes containing the word examples:
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)