Last Updated：2025/12/04

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(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.

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profinite group

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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.

Japanese Meaning

離散有限群の逆システムの逆極限に同型な位相群、すなわちストーン空間である位相群

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When studying Galois cohomology, one often encounters a profinite group acting continuously on a discrete module.

Google Translation / DeepL Translation

ガロアコホモロジーを研究するとき、しばしば有限群の逆系の逆極限として表される位相群が離散加群上で連続に作用していることに出会う。

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Sense（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.

Google Translation / DeepL Translation

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profinite groups

（ plural ）

Details

profinite group

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profinite group

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