Multiplicative group of integers modulo n

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Multiplicative group of integers modulo n

Quality:

Multiplicative group of integers modulo n - group of units of the ring of integers modulo n. Article “Multiplicative group of integers modulo n” in English Wikipedia has 35.8 points for quality (as of July 1, 2025). The article contains 8 references and 13 sections.

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

Since the creation of article “Multiplicative group of integers modulo n”, its content was written by 81 registered users of English Wikipedia and edited by 179 registered Wikipedia users in all languages.

The article is cited 57 times in English Wikipedia and cited 206 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #17963 in November 2014
  • Global: #37447 in November 2014

The highest popularity rank from 2008:

  • Local (English): #12650 in December 2014
  • Global: #30604 in December 2014

There are 8 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 July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

Languages with the highest quality

#LanguageQuality gradeQuality score
1English (en)
Multiplicative group of integers modulo n
35.7966
2Chinese (zh)
整数模n乘法群
32.2283
3Russian (ru)
Мультипликативная группа кольца вычетов
30.5049
4Ukrainian (uk)
Мультиплікативна група кільця лишків за модулем n
22.5384
5Spanish (es)
Grupo multiplicativo de enteros módulo n
19.3352
6German (de)
Prime Restklassengruppe
9.9904
7Vietnamese (vi)
Nhóm nhân các số nguyên modulo n
6.942
8Hebrew (he)
חבורת אוילר
4.8951
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 "Multiplicative group of integers modulo n" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Multiplicative group of integers modulo n
1 312 161
2Russian (ru)
Мультипликативная группа кольца вычетов
230 358
3German (de)
Prime Restklassengruppe
194 292
4Chinese (zh)
整数模n乘法群
70 832
5Hebrew (he)
חבורת אוילר
39 141
6Vietnamese (vi)
Nhóm nhân các số nguyên modulo n
18 622
7Ukrainian (uk)
Мультиплікативна група кільця лишків за модулем n
12 533
8Spanish (es)
Grupo multiplicativo de enteros módulo n
9 499
More...

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

Most popular in June 2025

The most popular language versions of the article "Multiplicative group of integers modulo n" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Multiplicative group of integers modulo n
3 874
2Russian (ru)
Мультипликативная группа кольца вычетов
642
3German (de)
Prime Restklassengruppe
265
4Chinese (zh)
整数模n乘法群
203
5Hebrew (he)
חבורת אוילר
91
6Spanish (es)
Grupo multiplicativo de enteros módulo n
35
7Vietnamese (vi)
Nhóm nhân các số nguyên modulo n
23
8Ukrainian (uk)
Мультиплікативна група кільця лишків за модулем n
16
More...

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

The highest AI

Language versions of the article "Multiplicative group of integers modulo n" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Multiplicative group of integers modulo n
81
2German (de)
Prime Restklassengruppe
28
3Russian (ru)
Мультипликативная группа кольца вычетов
20
4Hebrew (he)
חבורת אוילר
19
5Chinese (zh)
整数模n乘法群
9
6Ukrainian (uk)
Мультиплікативна група кільця лишків за модулем n
8
7Vietnamese (vi)
Nhóm nhân các số nguyên modulo n
8
8Spanish (es)
Grupo multiplicativo de enteros módulo n
6
More...

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

The highest AI in June 2025

Language versions of the article "Multiplicative group of integers modulo n" with the highest AI in June 2025
#LanguageAI awardRelative AI
1German (de)
Prime Restklassengruppe
0
2English (en)
Multiplicative group of integers modulo n
0
3Spanish (es)
Grupo multiplicativo de enteros módulo n
0
4Hebrew (he)
חבורת אוילר
0
5Russian (ru)
Мультипликативная группа кольца вычетов
0
6Ukrainian (uk)
Мультиплікативна група кільця лишків за модулем n
0
7Vietnamese (vi)
Nhóm nhân các số nguyên modulo n
0
8Chinese (zh)
整数模n乘法群
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 "Multiplicative group of integers modulo n" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Multiplicative group of integers modulo n
57
2Russian (ru)
Мультипликативная группа кольца вычетов
50
3Hebrew (he)
חבורת אוילר
33
4German (de)
Prime Restklassengruppe
30
5Chinese (zh)
整数模n乘法群
16
6Ukrainian (uk)
Мультиплікативна група кільця лишків за модулем n
8
7Spanish (es)
Grupo multiplicativo de enteros módulo n
6
8Vietnamese (vi)
Nhóm nhân các số nguyên modulo n
6
More...

Scores

Estimated value for Wikipedia:
English:
Global:
Popularity in June 2025:
English:
Global:
Popularity in all years:
English:
Global:
Authors in June 2025:
English:
Global:
Registered authors in all years:
English:
Global:
Citations:
English:
Global:

Quality measures

Interwikis

#LanguageValue
deGerman
Prime Restklassengruppe
enEnglish
Multiplicative group of integers modulo n
esSpanish
Grupo multiplicativo de enteros módulo n
heHebrew
חבורת אוילר
ruRussian
Мультипликативная группа кольца вычетов
ukUkrainian
Мультиплікативна група кільця лишків за модулем n
viVietnamese
Nhóm nhân các số nguyên modulo n
zhChinese
整数模n乘法群

Popularity rank trends

Best Rank English:
#12650
12.2014
Global:
#30604
12.2014

AI rank trends

Best Rank English:
#17963
11.2014
Global:
#37447
11.2014

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Multiplicative group of integers modulo n from Wikipedia articles about Eulers totient function, Primitive root modulo n, Eulers theorem, Diffie–Hellman key exchange and Multiplicative group. Whereas reading the article about Multiplicative group of integers modulo n people most often go to Wikipedia articles on Modular arithmetic, Primitive root modulo n, Congruence of integers, Eulers totient function and Cyclic group.

Cumulative results of quality and popularity of the Wikipedia article

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

News from 21 February 2026

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In English Wikipedia the most popular articles on that day were: Eric Dane, Alysa Liu, Rebecca Gayheart, Jeffrey Epstein, 2026 Winter Olympics, Eileen Gu, John F. Kennedy Jr., Carolyn Bessette Kennedy, Deaths in 2026, Johannes Høsflot Klæbo.

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 July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information