Definitions for abelian group
abelian group

Princeton's WordNetRate this definition:0.0 / 0 votes

1. Abelian group, commutative groupnoun

   a group that satisfies the commutative law

WiktionaryRate this definition:0.0 / 0 votes

1. abelian groupnoun

   a group in which the group operation is commutative

WikipediaRate this definition:0.0 / 0 votes

1. Abelian group

   In mathematics, 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 the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel.The concept of an abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified.

WikidataRate this definition:0.0 / 0 votes

1. 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.

Matched Categories

1. • Group

How to pronounce abelian group?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say abelian group in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of abelian group in Chaldean Numerology is: 8

2. Pythagorean Numerology

   The numerical value of abelian group in Pythagorean Numerology is: 4

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=abelian group
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Abelian_Group
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Abelian_Group
4. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=abelian group