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Integral representations for the alternating groups

Author: Udo Riese
Journal: Proc. Amer. Math. Soc. 130 (2002), 3515-3518
MSC (2000): Primary 20C10, 20C30
Published electronically: May 1, 2002
MathSciNet review: 1918827
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Abstract: We show that every complex representation of an alternating group can be realized over the ring of integers of a ``small'' abelian number field.

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

  • 1. G. Cliff, J. Ritter and A. Weiss, Group representations and integrality, J. Reine Angew. Math. 426 (1992), 193-202. MR 93f:20011
  • 2. C.W. Curtis and I. Reiner, Methods of representation theory, I, Wiley, New York, 1981. MR 82i:20001; reprint MR 90k:20001
  • 3. G. James and A. Kerber, The representation theory of the symmetric groups, Addison-Wesley, London, 1981. MR 83k:20003
  • 4. W. Knapp and P. Schmid, An extension theorem for integral representations, J. Austral. Math. Soc. (Series A) 63 (1997), 1-15. MR 98m:20014
  • 5. H. Leopoldt, Zur Geschlechtertheorie in abelschen Zahlkörpern, Math. Nachrichten 9 (1953), 351-362. MR 15:14d
  • 6. U. Riese, On integral representations for SL$(2,q)$, J. Algebra 242 (2001), 729-739.
  • 7. U. Riese and P. Schmid, Schur indices and Schur groups, II, J. Algebra 182 (1996), 183-200. MR 97e:20009
  • 8. F. Terada, A principal ideal theorem in the genus fields, Tôhoku Math. J. 23 (1971), 697-718. MR 46:5285

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Additional Information

Udo Riese
Affiliation: Universität Tübingen, Mathematisches Institut, Auf der Morgenstelle 10, D-72076 Tübingen, Germany

Received by editor(s): May 3, 2001
Received by editor(s) in revised form: July 30, 2001
Published electronically: May 1, 2002
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2002 American Mathematical Society

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