commutative group

8.4

A set with a rule to combine items where the order does not matter

noun
/kəˈmjuːtətɪv ɡruːp/

Specialized

: grupo conmutativo

The set of integers with addition forms a classic example of a commutative group.

Examples

In a commutative group, a + b is always equal to b + a.
Every commutative group is also called an abelian group.
A commutative group is fundamental in abstract algebra.
In a commutative group, the operation is independent of order.
The set of integers with addition forms a classic example of a commutative group.
In a commutative group, a + b is always equal to b + a.
Every commutative group is also called an abelian group.

Synonyms

Abelian group

vscommutative group

Specialized

9.9

A set with a combining rule where order does not change the result

is the same property but expressed as a descriptive phrase not a named term

Surface Forms

commutative group singular

commutative groups plural

Morphology

commutative + group

The meaning is directly derivable from composing 'commutative' (order of operation irrelevant) with 'group' (a set with an operation): it literally denotes a group whose operation is commutative. Although it is a technical mathematical term, the modifier+noun composition is transparent and would be understandable to a learner who knows both constituents.

Etymology

Commutative group gives a simple picture: the word commutative suggests 'swapping' and group means a collection of things. So a commutative group is a collection where you can change the 'order' of operations and still get the same result, for example 2 + 3 = 3 + 2.