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Meaning of "Abelian group" in the English dictionary

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DICTIONARY
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ETYMOLOGY OF THE WORD ABELIAN GROUP

Named after Niels Henrik Abel (1802–29), Norwegian mathematician.
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Etymology is the study of the origin of words and their changes in structure and significance.
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PRONUNCIATION OF ABELIAN GROUP

Abelian group  [əˈbiːlɪən] play
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GRAMMATICAL CATEGORY OF ABELIAN GROUP

noun
adjective
verb
adverb
pronoun
preposition
conjunction
determiner
exclamation
Abelian group is a noun.
A noun is a type of word the meaning of which determines reality. Nouns provide the names for all things: people, objects, sensations, feelings, etc.

WHAT DOES ABELIAN GROUP MEAN IN ENGLISH?

Abelian group

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on their order. Abelian groups generalize the arithmetic of addition of integers. They are named after Niels Henrik Abel. The concept of an abelian group is one of the first concepts encountered in undergraduate abstract algebra, with many other basic objects, such as a module and a vector space, being its refinements. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood. On the other hand, the theory of infinite abelian groups is an area of current research.

Definition of Abelian group in the English dictionary

The definition of Abelian group in the dictionary is a group the defined binary operation of which is commutative: if a and b are members of an Abelian group then ab = ba.

WORDS THAT RHYME WITH ABELIAN GROUP


anthelion
æntˈhiːlɪən
aphelian
æpˈhiːlɪən
aphelion
æpˈhiːlɪən
Aristotelian
ˌærɪstəˈtiːlɪən
Aurelian
ɔːˈriːlɪən
Caelian
ˈsiːlɪən
Chamaeleon
kəˈmiːlɪən
chameleon
kəˈmiːlɪən
cornelian
kɔːˈniːlɪən
Delian
ˈdiːlɪən
epitrachelion
ˌɛpɪtrəˈkiːlɪən
Karelian
kəˈriːlɪən
Mendelian
mɛnˈdiːlɪən
Mephistophelian
ˌmefɪstəˈfiːlɪən
Mingrelian
mɪŋˈɡriːlɪən
mycelian
maɪˈsiːlɪən
obelion
əʊˈbiːlɪən
parhelion
pɑːˈhiːlɪən
Pelion
ˈpiːlɪən
perihelion
ˌpɛrɪˈhiːlɪən

WORDS THAT BEGIN LIKE ABELIAN GROUP

Abednego
Abel
Abelard
abele
abelia
Abelian
abelmosk
Abelson
Abeokuta
aber
Abercrombie
Aberdare
Aberdeen
Aberdeen Angus
Aberdeen terrier
Aberdeenshire
aberdevine
Aberdonian
Aberfan

WORDS THAT END LIKE ABELIAN GROUP

age group
buying group
control group
discussion group
focus group
group
house group
in-group
interest group
media group
minority group
newsgroup
playgroup
public-interest group
splinter group
subgroup
support group
target group
user group
workgroup
working group

Synonyms and antonyms of Abelian group in the English dictionary of synonyms

SYNONYMS

Translation of «Abelian group» into 25 languages

TRANSLATOR
online translator

TRANSLATION OF ABELIAN GROUP

Find out the translation of Abelian group to 25 languages with our English multilingual translator.
The translations of Abelian group from English to other languages presented in this section have been obtained through automatic statistical translation; where the essential translation unit is the word «Abelian group» in English.

Translator English - Chinese

阿贝尔群
1,325 millions of speakers

Translator English - Spanish

grupo abeliano
570 millions of speakers

English

Abelian group
510 millions of speakers

Translator English - Hindi

abelian समूह
380 millions of speakers
ar

Translator English - Arabic

مجموعة ابليان
280 millions of speakers

Translator English - Russian

абелева группа
278 millions of speakers

Translator English - Portuguese

grupo abeliano
270 millions of speakers

Translator English - Bengali

আবেলিয়ান গ্রুপ
260 millions of speakers

Translator English - French

groupe abélien
220 millions of speakers

Translator English - Malay

Kumpulan Abelian
190 millions of speakers

Translator English - German

abelschen Gruppe
180 millions of speakers

Translator English - Japanese

アーベル群
130 millions of speakers

Translator English - Korean

아벨 그룹
85 millions of speakers

Translator English - Javanese

Kelompok Abelian
85 millions of speakers
vi

Translator English - Vietnamese

nhóm abelian
80 millions of speakers

Translator English - Tamil

ஆபேலிய குழு
75 millions of speakers

Translator English - Marathi

आबेलियन गट
75 millions of speakers

Translator English - Turkish

Abelian grubu
70 millions of speakers

Translator English - Italian

gruppo abeliano
65 millions of speakers

Translator English - Polish

abelowa
50 millions of speakers

Translator English - Ukrainian

абелева група
40 millions of speakers

Translator English - Romanian

grup abelian
30 millions of speakers
el

Translator English - Greek

αβελιανή ομάδα
15 millions of speakers
af

Translator English - Afrikaans

Abelse groep
14 millions of speakers
sv

Translator English - Swedish

abelska gruppen
10 millions of speakers
no

Translator English - Norwegian

abelsk gruppe
5 millions of speakers

Trends of use of Abelian group

TRENDS

TENDENCIES OF USE OF THE TERM «ABELIAN GROUP»

The term «Abelian group» is regularly used and occupies the 84.792 position in our list of most widely used terms in the English dictionary.
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100%
FREQUENCY
Regularly used
61
/100
The map shown above gives the frequency of use of the term «Abelian group» in the different countries.
Principal search tendencies and common uses of Abelian group
List of principal searches undertaken by users to access our English online dictionary and most widely used expressions with the word «Abelian group».

FREQUENCY OF USE OF THE TERM «ABELIAN GROUP» OVER TIME

The graph expresses the annual evolution of the frequency of use of the word «Abelian group» during the past 500 years. Its implementation is based on analysing how often the term «Abelian group» appears in digitalised printed sources in English between the year 1500 and the present day.

Examples of use in the English literature, quotes and news about Abelian group

EXAMPLES

10 ENGLISH BOOKS RELATING TO «ABELIAN GROUP»

Discover the use of Abelian group in the following bibliographical selection. Books relating to Abelian group and brief extracts from same to provide context of its use in English literature.
1
Exercises in Abelian Group Theory
This book, in some sense, began to be written by the first author in 1983, when optional lectures on Abelian groups were held at the Fac ulty of Mathematics and Computer Science,'Babes-Bolyai' University in Cluj-Napoca, Romania.
Grigore Calugareanu, 2003
2
Abelian Group Theory and Related Topics
This text presents the reader with a window on the frontier of the active research area of abelian groups.
Rüdiger Göbel, Paul Hill, Wolfgang Liebert, 1994
3
Modules Over the Integral Group Ring of a Non-abelian Group ...
If $p,q$ are primes with $p\equiv 1$ $({\rm mod}\,q)$ there is a unique nonabelian group $G$ of order $pq$.
Lee Klingler, 1986
4
Abelian Groups
This volume contains information offered at the international conference held in Curacao, Netherlands Antilles. It presents the latest developments in the most active areas of abelian groups, particularly in torsion-free abelian groups.
Laszlo Fuchs, Rudiger Gobel, 1993
5
Abelian Group Theory: Proceedings of the 1987 Perth ...
It has finite A-rank if / can be chosen to be finite. Primarily, Arnold and Lady were interested in obtaining a generalization of Baer's Lemma. In order to facilitate this, they investigated when an abelian group A has the following two properties: (I) ...
László Fuchs, Rüdiger Göbel, Phillip Schultz, 1989
6
Rigidity in Higher Rank Abelian Group Actions: Volume 1, ...
This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory.
Anatole Katok, Viorel Niţică, 2011
7
Non-Abelian Homological Algebra and Its Applications
It will be the aim of this book based on the results of researchers of A. Razmadze Mathematical Institute of the Georgian Academy of Sciences devoted to non-abelian homological algebra.
Hvedri Inassaridze, 1997
8
Topics in Factorization of Abelian Groups
We say that the finite abelian group G has the Redei property if from each factorization G = AB it follows that A or B does not span the whole of G. In 1995, studying a problem in Fourier analysis R. Tijdeman conjectured that finite cyclic groups ...
Sandor Szabo, 2004
9
Partially Ordered Abelian Groups with Interpolation
This is a reprint of the 1986 original. (SUR
Kenneth R. Goodearl, 2010
10
Complex Tori and Abelian Varieties
Standard theorems about abelian varieties are proved, and moduli spaces are discussed. Recent results on the geometry and topology of some subvarieties of a complex torus are also included. The book contains numerous examples and exercises.
Olivier Debarre, 2005

4 NEWS ITEMS WHICH INCLUDE THE TERM «ABELIAN GROUP»

Find out what the national and international press are talking about and how the term Abelian group is used in the context of the following news items.
1
A basic history of BASIC on its 50th birthday
E) The word LET came from our mathematics background, because we are always saying things like "Let G be an Abelian Group." Furthermore ... «Gamasutra, May 14»
2
Answers to Simon Singh's maths humour challenge
The punchline is a pun, because it sounds like "an abelian group". The elements in an abelian group are commutative, which means that ... «The Guardian, Oct 13»
3
Amazing Rope Trick
... I love this trick because it is the most concrete demonstration I have ever seen of the difference between an abelian and non-abelian group. «Scientific American, Sep 13»
4
Faculty Close-Up: Visiting Professor Zbigniew Oziewicz is …
... Frobenius algebra, the Hilbert-Schmidt spaces, abelian group of endofunctors and other topics that only a mathematician could appreciate. «UTSA Today, Feb 09»

REFERENCE
« EDUCALINGO. Abelian group [online]. Available <https://educalingo.com/en/dic-en/abelian-group>. Apr 2024 ».
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