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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Induction and structure theorems for Grothendieck and Witt rings of orthogonal representations of finite groups


Author: Andreas Dress
Journal: Bull. Amer. Math. Soc. 79 (1973), 741-745
MSC (1970): Primary 15A63, 16A54, 18F25; Secondary 20C99, 20J99, 57D65
MathSciNet review: 0342599
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  • 1. Andreas W. M. Dress, Notes on the theory of representations of finite groups. Part I: The Burnside ring of a finite group and some AGN-applications, Universität Bielefeld, Fakultät für Mathematik, Bielefeld, 1971. With the aid of lecture notes, taken by Manfred Küchler. MR 0360771 (50 #13218)
  • 2. Andreas W. M. Dress, Contributions to the theory of induced representations, Algebraic 𝐾-theory, II: “Classical” algebraic 𝐾-theory and connections with arithmetic (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Springer, Berlin, 1973, pp. 183–240. Lecture Notes in Math., Vol. 342. MR 0384917 (52 #5787)
  • 3. A. Fröhlich and A. M. McEvett, The representation of groups by automorphisms of forms, J. Algebra 12 (1969), 114–133. MR 0240217 (39 #1569)
  • 4. A. Fröhlich, Orthogonal and symplectic representations of groups, Proc. London Math. Soc. (3) 24 (1972), 470–506. MR 0308248 (46 #7362)
  • 5. J. A. Green, Axiomatic representation theory for finite groups, J. Pure Appl. Algebra 1 (1971), no. 1, 41–77. MR 0279208 (43 #4931)
  • 6. Manfred Knebusch, Grothendieck- und Wittringe von nichtausgearteten symmetrischen Bilinearformen, S.-B. Heidelberger Akad. Wiss. Math.-Natur. Kl. 1969/70 (1969/1970), 93–157 (German). MR 0271118 (42 #6001)
  • 7. Daniel Quillen, The Adams conjecture, Topology 10 (1971), 67–80. MR 0279804 (43 #5525)
  • 8. Winfried Scharlau, Induction theorems and the structure of the Witt group, Invent. Math. 11 (1970), 37–44. MR 0292752 (45 #1834)
  • 9. Richard G. Swan, 𝐾-theory of finite groups and orders, Lecture Notes in Mathematics, Vol. 149, Springer-Verlag, Berlin-New York, 1970. MR 0308195 (46 #7310)
  • 10. Richard G. Swan, Induced representations and projective modules, Ann. of Math. (2) 71 (1960), 552–578. MR 0138688 (25 #2131)
  • 11. C. T. C. Wall, Foundations of algebraic 𝐿-theory, Algebraic 𝐾-theory, III: Hermitian 𝐾-theory and geometric applications (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Springer, Berlin, 1973, pp. 266–300. Lecture Notes in Math., Vol. 343. MR 0357550 (50 #10018)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1973-13291-4
PII: S 0002-9904(1973)13291-4