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# Abelian group

## Definition of the noun abelian group

What does abelian group mean as a name of something?

noun

1. a group that satisfies the commutative law

## Explanation

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.

• also known as 阿贝尔群

## Printed dictionaries and other books with definitions for Abelian group

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### The Penguin Dictionary of Mathematics (2008)

Fourth edition by David Nelson

a ° b=b ° a for every pair of elements a, b in G, then the group is said to be commutative or Abelian (see Abelian group). So the set of integers with the operation of addition forms ...

### CRC Concise Encyclopedia of Mathematics, Second Edition (2002)

by Eric W. Weisstein

See also ABELIAN GROUP, CATEGORY Abelian Group References Freyd, P. Abelian Categories: An Introduction to the Theory of Functors. New York: Harper & Row, 1964. Grothendieck, A. "Sur quelques points d'alge`bre homologique.

### Encyclopaedia of Mathematics (1989)

by Michiel Hazewinkel

Let M be an Abelian group, let G(K / k) be the Galois group of an extension K / k and suppose G(K / k) acts on M\ the Galois cohomology groups will then be the cohomology groups H"(K /k, M) = H"(G(K / k), M), n>0, defined by the complex (C, d) ...

### Encyclopedia of Algorithms (2008)

by Ming-Yang Kao

Keywords and Synonyms Generalization of Abelian stabilizer problem; Generalization of Simon's problem Problem Definition The Abelian hidden subgroup problem is the problem of finding generators for a subgroup K of an Abelian group ...

### The Relational Database Dictionary, Extended Edition (2008)

by Christopher Date

Abelian group Seegroup (mathematics). absolute complement See complement (set theory). absorption Let operators OpC and ...

### Dictionary of Classical and Theoretical Mathematics (2001)

by Catherine Cavagnaro, William T. Haight, II

form an Abelian group; the product is given by disjoint union. The identity element is the class given by the empty set. The inverse of the ...

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