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AbelianGroup

AbelianGroup
represents the direct product of the cyclic groups of degrees .
  • AbelianGroup is represented by default as a permutation group on the points .
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:
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Permutation generators of an Abelian group:
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Elements of a permutation representation of an Abelian group:
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Direct product of any number of cyclic groups of any degrees:
For nonzero degrees, the order of AbelianGroup is the product of the :
A group AbelianGroup 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:
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