This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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Group Theory
Mathematica 8 introduces a coherent collection of algorithms and data structures for working with permutation groups. Building upon Mathematica's proven symbolic architecture, permutations can operate on group-theoretical data structures, as well as on arbitrary symbolic Mathematica expressions. State-of-the-art algorithms enable the efficient manipulation of very large groups. Commonly used groups are conveniently represented as built-in objects.
Group Representations
PermutationGroup permutation group object
Enumeration of Elements
GroupOrder number of elements in a group
GroupElements list of elements of a group
GroupElementQ test membership of an element in a group
GroupElementPosition locate element in a group
Description of a Group
GroupGenerators list of generators of a group
GroupMultiplicationTable all products of elements in a group
CayleyGraph graph representation of a group and a set of generators
GroupStabilizerChain strong generators and base for a group
GroupActionBase option to specify a base for a (permutation) group
Computations with a Group
GroupOrbits orbits of points under a group
GroupStabilizer pointwise stabilizer subgroup
GroupSetwiseStabilizer setwise stabilizer subgroup
RightCosetRepresentative smallest element in a coset
GroupCentralizer centralizer of an element in a group
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