Abelian group
- noun
- /əˈbiːliən ɡruːp/
- Specialized
:
grupo abeliano
- One important example of an abelian group is the set of real numbers with addition, where the sum remains the same regardless of the order.
Examples
-
If you know what a group is, you will observe that addition modulo n is an abelian group, with the congruence classes as elements.
Blog text (31) -
So R under addition is an abelian group, Abelian group.
-
When I was very young my teachers told me that if I deal with what is known abelian groups, I write plus.
-
However, those where you can commute, those called abelian groups and those where you cannot, those are non abelian groups.
-
More interestingly, multiplication on the classes coprime to n is also an abelian group, though its properties are less obvious.
Blog text (31) -
So this theorem gives you the characterization of subsets in general abelian groups that have small doubling.
-
Cielo theorems, applications of the Cielo theory, free abelian groups, free groups, group presentations.
-
The set of integers under addition forms an abelian group because changing the order of the numbers does not affect the sum.
-
In mathematics, an abelian group is defined as a group where the operation is commutative, meaning a * b = b * a for any elements a and b.
Synonyms
A set with a rule to combine items where the order does not matter
Surface Forms
Morphology
The noun phrase is a direct adjective + noun composition: if a learner knows 'abelian' (i.e. commutative) and 'group' (a mathematical set with an operation), they can infer an 'Abelian group' is a group whose operation is commutative. Although 'abelian' is an eponymous technical term, the meaning follows straightforward compositional semantics and is thus predictable to someone who knows both constituents.
Etymology
Abelian group is named after the mathematician Niels Abel. It describes a group where the order of combining elements does not matter, for example 2 plus 3 is the same as 3 plus 2, so it means a group that is 'order does not matter'.
