gives the number of finite Abelian groups of order n.
- Integer mathematical function, suitable for both symbolic and numerical manipulation.
- FiniteAbelianGroupCount automatically threads over lists.
Examplesopen allclose all
FiniteAbelianGroupCount threads element-wise over lists:
Properties & Relations (6)
FiniteAbelianGroupCount[n] gives the number of Abelian groups of order n:
FiniteGroupCount[n] gives the number of groups of order n, both Abelian and non-Abelian:
For low orders, FiniteGroupData lists explicit representative Abelian groups of a given order:
The number of finite Abelian groups can be found using PartitionsP:
FiniteAbelianGroupCount[n] depends only on prime exponents of n:
FiniteAbelianGroupCount is a multiplicative function:
Possible Issues (1)
Neat Examples (1)
Successive differences of FiniteAbelianGroupCount modulo 2: