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On the projective class group of cyclic groups of prime power order

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Commentarii Mathematici Helvetici

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Bibliography

  1. Artin, E. andTate, J.,Class Field Theory, Benjamin (1968).

  2. Bass, H.,Algebraic K-Theory, Benjamin (1968).

  3. Bass, H. andMurthy, P.,Grothendieck groups and Picard groups of abelian group rings, Ann. of Math.86 (1967), 16–73.

    Article  MathSciNet  Google Scholar 

  4. Borevich, Z. I. andShafarevich, J. R.,Number Theory, Academic Press, New York (1966).

    MATH  Google Scholar 

  5. Fröhlich, A,On the classgroup of integral group rings of finite abelian groups I, II, Mathematika16 (1969), 143–152 and19 (1972), 51–56.

    MathSciNet  MATH  Google Scholar 

  6. Galovich, S.,The class group of a cyclic p-group, Journal of Algebra30 (1974), 368–387.

    Article  MATH  MathSciNet  Google Scholar 

  7. Hasse, H.,Vorlesungen über Klassenkörpertheorie, Physica Verlag, Würzburg (1967).

    MATH  Google Scholar 

  8. Hasse, H.,Ueber die Klassenzahl abelscher Zahlkörper, Akademie Verlag, Berlin (1952).

    MATH  Google Scholar 

  9. Hecke, E.,Vorlesungen über die Theorie der algebraischen Zahlen, Chelsea, New York (1948).

    MATH  Google Scholar 

  10. Higman, G.,The units of group rings, Proc. London Math. Soc.,46 (1940), 231–248.

    MATH  MathSciNet  Google Scholar 

  11. Iwasawa, K.,A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg20 (1956), 257–258.

    MATH  MathSciNet  Google Scholar 

  12. Iwasawa, K.,On Γ-extensions of algebraic number fields, Bull. Amer. Math. Soc.65 (1959), 183–226.

    Article  MATH  MathSciNet  Google Scholar 

  13. Iwasawa, K.,On the theory of cyclotomic fields, Ann. of Math.70 (1959), 530–561.

    Article  MathSciNet  Google Scholar 

  14. Iwasawa, K.,On some modules in the theory of cyclotomic fields, J. Math. Soc. Japan16 (1964), 42–82.

    MATH  MathSciNet  Google Scholar 

  15. Iwasawa, K. andSims, C.,Computation of invariants in the theory of cyclotomic fields, J. Math. Soc. Japan18 (1966), 86–96.

    Article  MATH  MathSciNet  Google Scholar 

  16. Lang, S.,Algebraic number theory, Addison-Wesley, 2nd edition (1970).

  17. Milnor, J.,Introduction to algebraic K-theory, Annals of Math. Studies 72, Princeton Univ. Press (1971).

  18. Rim, D. S.,Modules over finite groups, Ann. of Math.69 (1959), 700–712.

    Article  MathSciNet  Google Scholar 

  19. Serre, J. P.,Classes des corps cyclotomiques, Séminaire Bourbaki, Exposé 174 (1958/1959).

  20. Ullom, S.,A note on the class group of integral group rings of some cyclic groups, Mathematika17 (1970), 79–81.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institut de Mathématiques, 2-4, rue du Lièvre, 1211, Genève

    Michel A. Kervaire & M. Pavaman Murthy

  2. University of Chicago, Chicago, Illinois

    Michel A. Kervaire & M. Pavaman Murthy

Authors
  1. Michel A. Kervaire
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  2. M. Pavaman Murthy
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Dedicated to Beno Eckmann on the occasion of his sixtieth birthday.

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Kervaire, M.A., Murthy, M.P. On the projective class group of cyclic groups of prime power order. Commentarii Mathematici Helvetici 52, 415–452 (1977). https://doi.org/10.1007/BF02567377

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  • DOI: https://doi.org/10.1007/BF02567377

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