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Abelian Group (Noun)

Meaning

A group that satisfies the commutative law.

Classification

Nouns denoting cognitive processes and contents.

Examples

  • The cyclic groups form an important class of abelian groups and play a key role in the structure theory of abelian groups.
  • Any subgroup of an abelian group is also abelian.
  • It can be shown that any free abelian group has a basis.
  • For a positive integer n, the abelian group ℤ/nℤ has exactly n elements.
  • If H and K are two subgroups of an abelian group G such that HK is a subgroup, then HK is an abelian group.

Synonyms

  • Commutative Group

Hypernyms

  • Mathematical Group
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