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Profinite group

In mathematics, a profinite group is a topological group that is in a certain sense assembled from a system of finite groups.

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Overview

Definition

Examples

Properties and facts

Ind-finite groups

Projective profinite groups

Procyclic group

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Profinite group

Nodes95
Edges94
Triples112
Avg. degree1.98
Density0.021053
Components1

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Profinite group

Top relations

related to References · 49
Profinite group → Alexander, American Mathematical Society, Annals, Book Review, Bulletin, Cohomologie, Dan, Ergebnisse, Field, Folge, French, Fried, Galois, GR/0604399, GR/0604400, Grenzgebiete, Hendrik, II, ISBN, Jarden
related to Properties and facts · 21
Profinite group → According, As, Dan Segal, Every, Further, Furthermore, G/N, Haar, Hausdorff, If, Indeed, Jean-Pierre Serre, Nikolay Nikolov, Nikolov, Segal, Since, Suppose, The, Then, Therefore
related to Examples · 17
Profinite group → CW, F/K, Finite, For, Gal, Galois, In, It, Krull, L/K, Not, Specifically, The, The Galois, This, Waterhouse, Wolfgang Krull
related to Ind-finite groups · 6
Profinite group → By, In, Pontryagin, The, There, This
related to Profinite completion · 5
Profinite group → G/N, Given, It, The, There
is a · 4
Profinite group → Hausdorff, same as the topology arising from the p, topological group that is in a certain sense assembled from a system of finite groups.The idea of using a profinite group is to provide a, topological group that is isomorphic to the inverse limit of an inverse system of discrete finite groups
related to First definition (constructive) · 3
Profinite group → In, One, The
related to Projective profinite groups · 2
Profinite group → Projectivity, This
related to Second definition · 2
Profinite group → Hausdorff, Stone
related to Surjective systems · 2
Profinite group → In, Without

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Important terminology

profinite group groups displaystyle finite system inverse every galois generated limit topology finitely field subgroup mathbb homomorphisms surjective discrete index

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Profinite groupis atopological group that is in a certain sense assembled from a system of finite groups.The idea of using a profinite group is to provide a0.90text
Profinite groupis atopological group that is isomorphic to the inverse limit of an inverse system of discrete finite groups0.90text
Profinite groupis aHausdorff0.90text
Profinite groupis asame as the topology arising from the p0.90text
Profinite grouprelated to DefinitionProfinite0.60section
Profinite grouprelated to ExamplesFinite0.60section
Profinite grouprelated to ExamplesThe0.60section
Profinite grouprelated to ExamplesIt0.60section
Profinite grouprelated to ExamplesIn0.60section
Profinite grouprelated to ExamplesThis0.60section
Profinite grouprelated to ExamplesGalois0.60section
Profinite grouprelated to ExamplesThe Galois0.60section

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