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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.

Synonyms

  • Abelian Group

Hypernyms

  • Group
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