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High speed computation of group characters

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Abstract

This paper describes a practical procedure for computing the ordinary irreducible characters of finite groups (of orders up to 1000 or so). The novelty of the method consists of transposing the problem from the field of complex numbers into the field of integers modulop for a suitable primep. It is much easier to compute the modular characters in the latter field, and from these characters we can calculate the ordinary irreducible characters in algebraic form.

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References

  1. 1.

    Burnside, W.: Theory of groups of finite order,2nd ed. reprint. New York: Dover 1955.

  2. 2.

    Curtis, C. W., andI. Reiner: Representation theory of finite groups and associative algebras. New York: Wiley 1962.

  3. 3.

    Van Der Waerden, B. L.: Modern algebra, vol. 1. New York: Frederick Ungar 1949.

  4. 4.

    Vinogradov, I. M.: Elements of number theory. 5th ed. New York: Dover 1954.

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Dixon, J.D. High speed computation of group characters. Numer. Math. 10, 446–450 (1967). https://doi.org/10.1007/BF02162877

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Keywords

  • Mathematical Method
  • Complex Number
  • Finite Group
  • Irreducible Character
  • Speed Computation