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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Computing irreducible representations of groups
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by John D. Dixon PDF
Math. Comp. 24 (1970), 707-712 Request permission


How can you find a complete set of inequivalent irreducible (ordinary) representations of a finite group? The theory is classical but, except when the group was very small or had a rather special structure, the actual computations were prohibitive before the advent of high-speed computers; and there remain practical difficulties even for groups of relatively small orders $( \leqq 100)$. The present paper describes three techniques to help solve this problem. These are: the reduction of a reducible unitary representation into its irreducible components; the construction of a complete set of irreducible unitary representations from a single faithful representation; and the calculation of the precise values of a group character from values which have only been computed approximately.
    C. Brott & J. Neubüser, A Program for the Calculation of Characters and Representations of Finite Groups, Proc. Conf. Comput. Algebra (Oxford 1967), Pergamon Press, New York, 1969.
  • W. Burnside, Theory of groups of finite order, Dover Publications, Inc., New York, 1955. 2d ed. MR 0069818
  • John J. Cannon, Computers in group theory: A survey, Comm. ACM 12 (1969), 3–12. MR 0290613, DOI 10.1145/362835.362837
  • John D. Dixon, Problems in group theory, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1967. MR 0218428
  • John D. Dixon, High speed computation of group characters, Numer. Math. 10 (1967), 446–450. MR 224726, DOI 10.1007/BF02162877
  • Walter Feit, Characters of finite groups, W. A. Benjamin, Inc., New York-Amsterdam, 1967. MR 0219636
  • J. K. McKay, "A method for computing the simple character table of a finite group," in Computers in Mathematical Research, R. F. Churchhouse and J. C. Herz (Editors), NorthHolland, Amsterdam, 1968. MR 38 #1972. J. K. McKay, The Construction of the Character Table of a Finite Group from Generators and Relations, Proc. Conf. Comput. Algebra (Oxford 1967), Pergamon Press, New York, 1969. J. Neubüser, Investigations of Finite Groups on Computers, Proc. Conf. Comput. Algebra (Oxford 1967), Pergamon Press, New York, 1969. P. G. Rudd & E. R. Keown, The Computation of Irreducible Representations of Finite Groups of Order${2^n}$ $n \leqq 6$, Proc. Conf. Comput. Algebra (Oxford 1967) Pergamon Press, New York, 1969.
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Math. Comp. 24 (1970), 707-712
  • MSC: Primary 20.80; Secondary 65.00
  • DOI:
  • MathSciNet review: 0280611