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.