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Proceedings of the American Mathematical Society

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Characters of $ p$-groups

Author: Charles E. Ford
Journal: Proc. Amer. Math. Soc. 101 (1987), 595-601
MSC: Primary 20C15
MathSciNet review: 911015
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Abstract: The following theorem is proved for any prime $ p$:

Every irreducible rational represention of a finite $ p$-group is the difference of two transitive permutation representations.

Also given are two useful results about representations of $ p$-groups, which are known to experts in the field.

References [Enhancements On Off] (What's this?)

  • [1] Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1962. MR 0144979
  • [2] Walter Feit, Characters of finite groups, W. A. Benjamin, Inc., New York-Amsterdam, 1967. MR 0219636
  • [3] Charles Ford, Some results on the Schur index of a representation of a finite group., Canad. J. Math. 22 (1970), 626–640. MR 0260891
  • [4] Daniel Gorenstein, Finite groups, 2nd ed., Chelsea Publishing Co., New York, 1980. MR 569209
  • [5] Tsit-yuen Lam, Artin exponent of finite groups, J. Algebra 9 (1968), 94–119. MR 0224705
  • [6] Graeme Segal, Permutation representations of finite 𝑝-groups, Quart. J. Math. Oxford Ser. (2) 23 (1972), 375–381. MR 0322041
  • [7] Louis Solomon, The representation of finite groups in algebraic number fields, J. Math. Soc. Japan 13 (1961), 144–164. MR 0143822
  • [8] Ernst Witt, Die algebraische Struktur des Gruppenringes einer endlichen Gruppe über einem Zahlkörper, J. Reine Angew. Math. 190 (1952), 231–245 (German). MR 0053944
  • [9] Toshihiko Yamada, Characterization of the simple components of the group algebras over the 𝑝-adic number field, J. Math. Soc. Japan 23 (1971), 295–310. MR 0279210

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Keywords: Representation, $ p$-group, Schur index
Article copyright: © Copyright 1987 American Mathematical Society