Next: Finitely Generated Abelian Groups
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A generic (finite) abelian group can be created (using
GenericAbelianGroup) over any domain provided that
an identity and a group operation have been defined.
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Once created one can compute the structure of the group.
This is possible if the order of the group is known beforehand.
However, it is also possible to compute the structure of the group
from a user-supplied set of generators.
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Standard functions for creating subgroups and/or p-Sylow
subgroups are provided.
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Standard element operations like computing the order
or the discrete logarithm of an element are also provided.
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It is also possible
to compute the representation of any group element
in terms of a given set of generators of the group.