Closed-subgroup theorem

en

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Closed-subgroup theorem

Quality:

Closed subgroup theorem - theorem stating that, if H is a closed subgroup of a Lie group G, then H is an embedded Lie group with the relative topology being the same as the group topology. Article "Closed-subgroup theorem" in English Wikipedia has 51.5 points for quality (as of November 1, 2023). The article contains 31 references and 12 sections.

In this language version of Wikipedia the article has the best quality. Also, this article is the most popular in that language version.

In October 2023 the article "Closed-subgroup theorem" was edited by 1 authors in English Wikipedia and written by 3 authors in all languages.

Since the creation of article "Closed-subgroup theorem", its content was written by 32 registered users of English Wikipedia and edited by 46 registered Wikipedia users in all languages.

The article is cited 18 times in English Wikipedia and cited 26 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #14933 in July 2014
  • Global: #63710 in July 2014

The highest popularity rank from 2008:

  • Local (English): #646841 in August 2014
  • Global: #1149191 in August 2014

There are 4 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from November 1, 2023 (including revision history and pageviews for previous years).

下表顯示了最高品質的文章的語言版本。

Languages with the highest quality

#LanguageQuality gradeQuality score
1English (en)
Closed-subgroup theorem
51.458
2French (fr)
Théorème de Cartan-von Neumann
25.5475
3Ukrainian (uk)
Теорема про замкнуті підгрупи
4.3185
4German (de)
Satz von Cartan (Lie-Gruppen)
4.2566
More...

The following table shows the most popular language versions of the article.

Most popular in all the time

The most popular language versions of the article "Closed-subgroup theorem" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Closed-subgroup theorem
64 933
2German (de)
Satz von Cartan (Lie-Gruppen)
1 926
3Ukrainian (uk)
Теорема про замкнуті підгрупи
134
4French (fr)
Théorème de Cartan-von Neumann
122
More...

The following table shows the language versions of the article with the highest popularity in the last month.

Most popular in October 2023

The most popular language versions of the article "Closed-subgroup theorem" in October 2023
#LanguagePopularity awardRelative popularity
1English (en)
Closed-subgroup theorem
761
2French (fr)
Théorème de Cartan-von Neumann
43
3German (de)
Satz von Cartan (Lie-Gruppen)
22
4Ukrainian (uk)
Теорема про замкнуті підгрупи
5
More...

The following table shows the language versions of the article with the highest Authors’ Interest.

The highest AI

Language versions of the article "Closed-subgroup theorem" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Closed-subgroup theorem
32
2German (de)
Satz von Cartan (Lie-Gruppen)
9
3French (fr)
Théorème de Cartan-von Neumann
4
4Ukrainian (uk)
Теорема про замкнуті підгрупи
1
More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

The highest AI in October 2023

Language versions of the article "Closed-subgroup theorem" with the highest AI in October 2023
#LanguageAI awardRelative AI
1French (fr)
Théorème de Cartan-von Neumann
2
2English (en)
Closed-subgroup theorem
1
3German (de)
Satz von Cartan (Lie-Gruppen)
0
4Ukrainian (uk)
Теорема про замкнуті підгрупи
0
More...

The following table shows the language versions of the article with the highest number of citations.

The highest CI

Language versions of the article "Closed-subgroup theorem" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Closed-subgroup theorem
18
2German (de)
Satz von Cartan (Lie-Gruppen)
4
3French (fr)
Théorème de Cartan-von Neumann
4
4Ukrainian (uk)
Теорема про замкнуті підгрупи
0
More...

Scores

Estimated value for Wikipedia:
English:
Global:
Popularity in October 2023:
English:
Global:
Popularity in all years:
English:
Global:
Authors in October 2023:
English:
Global:
Registered authors in all years:
English:
Global:
Citations:
English:
Global:

Quality measures

Interwikis

#LanguageValue
deGerman
Satz von Cartan (Lie-Gruppen)
enEnglish
Closed-subgroup theorem
frFrench
Théorème de Cartan-von Neumann
ukUkrainian
Теорема про замкнуті підгрупи

Popularity rank trends

Best Rank English:
#646841
08.2014
Global:
#1149191
08.2014

AI rank trends

Best Rank English:
#14933
07.2014
Global:
#63710
07.2014

Languages comparison

Important global interconnections

Wikipedia readers most often find their way to information on Closed subgroup theorem from Wikipedia articles about Lie group, Cartans theorem, Élie Cartan, Lie group–Lie algebra correspondence and John von Neumann. Whereas reading the article about Closed subgroup theorem people most often go to Wikipedia articles on Topological group, Lie group, Cartans theorem, Lie group–Lie algebra correspondence and Embedding.

Cumulative results of quality and popularity of the Wikipedia article

List of Wikipedia articles in different languages (starting with the most popular):

News from 19 June 2024

On 19 June 2024 in multilingual Wikipedia, Internet users most often read articles on the following topics: UEFA Euro 2024, UEFA European Championship, Xherdan Shaqiri, Jamal Musiala, Cristiano Ronaldo, Albania, UEFA Euro 2020, İlkay Gündoğan, Inside Out 2, Juneteenth.

In English Wikipedia the most popular articles on that day were: Juneteenth, Willie Mays, UEFA Euro 2024, Xherdan Shaqiri, Jamal Musiala, Deaths in 2024, House of the Dragon, Inside Out 2, UEFA European Championship, Justin Timberlake.

About WikiRank

The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from November, 2023. When calculating current popularity and AI of articles data from October 2023 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2023... More information