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Mathematica > Mathematics and Algorithms > Discrete Mathematics > Group Theory > Named Groups > AbelianGroup >

BUILT-IN MATHEMATICA SYMBOL

AbelianGroup

represents the direct product of the cyclic groups of degrees

Number of elements of an Abelian group:

Permutation generators of an Abelian group:

Elements of a permutation representation of an Abelian group:

Number of elements of an Abelian group:

Out[1]=

Permutation generators of an Abelian group:

Out[1]=

Elements of a permutation representation of an Abelian group:

Out[1]=

Direct product of any number of cyclic groups of any degrees:

For nonzero degrees, the order of AbelianGroup

is the product of the

with p prime is called an elementary Abelian group. In such groups all nontrivial elements have order p:

The Cayley graph of the direct product of two cyclic groups resembles a torus: