SEARCH MATHEMATICA 8 DOCUMENTATION

THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.

Mathematica > Mathematics and Algorithms > Discrete Mathematics > Combinatorial Functions >

Built-in Mathematica Symbol

FiniteAbelianGroupCount

FiniteAbelianGroupCount[n]
gives the number of finite abelian groups of order n.

Integer mathematical function, suitable for both symbolic and numerical manipulation.

Table of values:

Evaluate for large arguments:

FiniteAbelianGroupCount threads element-wise over lists:

Number of non-abelian groups of order n:

Compare cumulative counts of even and odd number of abelian groups:

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:

FiniteAbelianGroupCount evaluates only for explicit integer values:

Use Simplify to find implicit integers in arguments:

Successive differences of FiniteAbelianGroupCount modulo 2: