Commutative Group (Noun)
Meaning
A group that satisfies the commutative law.
Classification
Nouns denoting cognitive processes and contents.
Examples
- The integers under addition form a commutative group because the order in which the integers are added does not affect the result.
- In a commutative group, each element can be associated with an inverse to produce an identity element.
- Real numbers with non-zero magnitude form a commutative group under multiplication due to their adherence to the commutative property.
- One way to establish the presence of a commutative group is by confirming the preservation of identity elements in every combination of the elements involved.
- Group properties also help describe complex entities and explain mathematical theorems which demonstrate operations involved within the boundaries of the established commutative group.