English Dictionary

profinite group

noun

(topology, category theory) A topological group that is isomorphic to the inverse limit of some inverse system of discrete finite groups; equivalently, a topological group that is also a Stone space.

A profinite group is a compact topological group that is the inverse limit of an inverse system of finite groups.

意味（1）

(topology, category theory) A topological group that is isomorphic to the inverse limit of some inverse system of discrete finite groups; equivalently, a topological group that is also a Stone space.

This proposition shows that to have a representation with big image of a profinite group, for example, a Galois group, we need to take a profinite topological ring A as a coefficient ring, like the p-adic integer ring Z ₚ.