Computation with permutation groups

ABSTRACT

The purpose of this paper is to provide an introduction to some computational techniques which have proved useful in the study of large permutation groups. In particular they have been used to study the Suzuki simple group of degree 1782 and order 448,345,497,600 and the simple group G2(5) of order 5,859,000,000 in a representation of degree 3906. Many of the algorithms discussed here are still in a developmental state and no claim is made that the most efficient solutions have been found.

REFERENCES

• 1: M. Hall: The Theory of Groups (New York: The Macmillan Company, 1959).
• 2: C. C. Sims: Determining the conjugacy classes of a permutation group, Proceeding of the Symposium on Computers in Algebra and Number Theory, American Mathematical Society, (1970), New York.
• 3: H. Wielandt: Finite Permutation Groups (New York: Academic Press, 1964).

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.2 DISCRETE MATHEMATICS
      G.2.1 Combinatorics
          Subjects: Permutations and combinations

Additional Classification:
  G. Mathematics of Computing
  G.2 DISCRETE MATHEMATICS
      G.2.2 Graph Theory

General Terms:
Algorithms, Theory