# abelian group

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Related to abelian group: group theory, vector space, Cyclic group

## a·be·li·an group

(ə-bē′lē-ən)
n.

[After Niels Henrik Abel (1802-1829), Norwegian mathematician.]

## Abelian group

(əˈbiːlɪən)
n
(Mathematics) a group the defined binary operation of which is commutative: if a and b are members of an Abelian group then ab = ba
[C19: named after Niels Henrik Abel (1802–29), Norwegian mathematician]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 Abelian group - a group that satisfies the commutative lawcommutative groupmathematical group, group - a set that is closed, associative, has an identity element and every element has an inverse
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Every finite Abelian group is determined by its endomorphism monoid in the class of all groups.
Then G/G' is an abelian group and G' is minimal with respect to this property.
It is clear that (NQ, +) is an abelian group and (NQ,.
In order to study self-dual abelian codes, it is therefore restricted to the group algebra [mathematical expression not reproducible], where A is an abelian group of odd order and B is a nontrivial abelian group of two power order.
Moreover, the notion of bond lattice comes from the study of Galois connections, and a natural action of set partitions that is analogous to the action of integers on any abelian group.
As we will see, he can follow the same strategy in any abelian group.
A subgroup H of an abelian group G is pure in G if nH = H (1 nG, where n is any non-zero integer.
n] of units modulo n, the abelian group [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and the affine group Aff([Z.
Sooryanarayana, Hamiltonian Distance Generating sets of an Abelian Group, Proceedings, National Seminar on Recent developments in applications of Mathematics held at Sri Padmavathi Mahila University, Tirupati, Andhra Pradesh, India, during 21-22, March 2005.
alpha]] ([alpha] [member of] C) forms an Abelian group with the Dirichlet series multiplication followed by a number of applications.
Cholewa (2) demonstrated that Skof's theorem is also valid if the relevant domain is replaced by an Abelian group.

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