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Proceedings of the American Mathematical Society

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Automorphisms of the integral group ring of $ S\sb{n}$


Author: Gary L. Peterson
Journal: Proc. Amer. Math. Soc. 59 (1976), 14-18
MSC: Primary 20C05
DOI: https://doi.org/10.1090/S0002-9939-1976-0412259-1
MathSciNet review: 0412259
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Abstract: In this paper it is shown that every normalized automorphism of the integral group ring of $ {S_n}$ can be written as a group automorphism followed by conjugation by a unit in the group algebra of $ {S_n}$ over the rationals.


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

  • [1] Hermann Boerner, Representations of groups. With special consideration for the needs of modern physics, Translated from the German by P. G. Murphy in cooperation with J. Mayer-Kalkschmidt and P. Carr. Second English edition, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1970. MR 0272911
  • [2] C. F. Brown, Automorphisms of integral group rings, Ph. D. Thesis, Michigan State University, 1971.
  • [3] G. L. Peterson, Automorphisms of integral group rings. I Arch. Math. (to appear).
  • [4] -, Automorphisms of integral group rings. II (to appear).
  • [5] W. R. Scott, Group theory, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0167513
  • [6] Sudarshan K. Sehgal, On the isomorphism of integral group rings. I, Canad. J. Math. 21 (1969), 410–413. MR 0255706, https://doi.org/10.4153/CJM-1969-044-9

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0412259-1
Keywords: Integral group ring, symmetric group, normalized automorphism, group automorphism, augmentation, class sum
Article copyright: © Copyright 1976 American Mathematical Society