Core Algorithms

Group Theory Algorithms

Mathematica 8 adds new functions and algorithms to work with permutations and permutation groups. This provides, for the first time in Mathematica, systematic access to the vast variety of groups that can be efficiently constructed by multiplication of a set of permutations.

  • Support for permutations in disjoint cyclic notation.
  • Support for groups generated by sets of permutations. Pre-stored generators for infinite families of groups and sporadic groups.
  • Visualization of groups as multiplication tables or Cayley graphs.
  • Computation of orbits, stabilizers, centralizers, coset representatives, etc.
Compute the Multiplication Table of a Group »Cayley Graph Representation of a Group »Points moved by increasing permutations in a group »
Orders of Groups with Random Generators »Compute the Conjugacy Class of an Element of a Permutation Group »Stabilizer Chain for the 3x3x3 Rubik Group »


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