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Definitions from WordNet

Definitions from the Web

Commutative Group

Description

A commutative group, in mathematics, is a group where the order in which two elements are combined does not affect the result. This means that the group operation is commutative, or that the elements can be swapped without changing the outcome.

Sample Sentences

As a noun:

1. The commutative group property is an important concept in abstract algebra.
2. In a commutative group, addition and multiplication operations are both commutative.
3. Examples of commutative groups include the integers under addition and the rational numbers under multiplication.

As an adjective:

1. A commutative group operation can be easily visualized using a commutative diagram.
2. The commutative group property allows for flexible rearrangements of terms.
3. By definition, a commutative group satisfies the commutative property.

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