# Abelian group

Also found in: Dictionary, Thesaurus, Wikipedia.
Related to Abelian group: group theory, vector space, Cyclic group

## Abelian group

[ə′bēl·yən ′grüp]
(mathematics)
A group whose binary operation is commutative; that is, ab = ba for each a and b in the group. Also known as commutative group.
References in periodicals archive ?
Examples of such groups are: finite Abelian groups ([12], Theorem 4.
To study self-dual abelian codes, it is sufficient to focus on [mathematical expression not reproducible], where A is an abelian group of odd order and B is a nontrivial abelian group of two power order.
2 If G is an abelian group of order n and n is divisible by m then there exists a subgroup of G with order m.
Infinite Abelian Groups Vol 1 New York: Academic Press.
Then (N, *) is an Abelian group with identity element [[xi].
3 A(n, H) and B(n, H) are the subgroups of an additive Abelian group G.
The above theorem can be expressed in the following way: The quadratic functional equation is stable for the pair (G, E), where G is an Abelian group and E is a Banach space.
The locally compact abelian group framework has two advantages, one general and the other specific.
Words obey the group laws a(bc) = ab(c), ai = ia = a, and aa' = a'a = i and the abelian group law ab = ba.
Therefore abelian groups are completely characterized as subtractive groupoids.
Q], the locally compact abelian group of unitary characters of the abelian additive group of g[.
So we consider partial dualization r' on H* = C [G] = C [N] x C [Q] where N is an abelian group and a self-dual Q-module.

Site: Follow: Share:
Open / Close