Skip to main content
SpringerLink
Log in

Projective class groups of integral group rings: a survey

  • Conference paper
  • First Online:
Orders and their Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1142))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Bass, Algebraic K-theory, Benjamin (1968).

    Google Scholar 

  2. S. Bentzen, Some numerical results on space forms (to appear).

    Google Scholar 

  3. S. Bentzen, I. Madsen, On the Swan subgroup of certain periodic groups, Math. Ann. 264 (1983), 447–474.

    Article  MathSciNet  MATH  Google Scholar 

  4. Ph. Cassou-Noguès, M. Taylor, Operations d’Adams et groupe des classes d’algèbre de groupe (to appear).

    Google Scholar 

  5. P. Draxl, Skew fields, London Math. Soc. lecture notes 81, Cambridge Univ. Press (1983).

    Google Scholar 

  6. S. Endo, T. Miyata, Quasi-permutation modules over finite groups, J. Math. Soc. Japan 25 (1973), 397–421.

    Article  MathSciNet  MATH  Google Scholar 

  7. S. Endo, T. Miyata, Quasi-permutation modules over finite groups II, J. Math. Soc. Japan 26 (1974), 698–713.

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Fröhlich, On the classgroup of integral group rings of finite abelian groups, Mathematika 16 (1969), 143–152.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Fröhlich, On the classgroup of integral group rings of finite abelian groups II, Mathematika 19 (1972), 51–56.

    Article  MathSciNet  MATH  Google Scholar 

  10. A. Fröhlich, Locally free modules over arithmetic orders, J. reine ang. Math. 274/275 (1975), 112–124.

    MathSciNet  MATH  Google Scholar 

  11. A. Fröhlich, M. Keating, S. Wilson, The class groups of quaternion and dihedral 2-groups, Mathematika 21 (1974), 64–71.

    Article  MathSciNet  MATH  Google Scholar 

  12. S. Galovich, I. Reiner, S. Ullom, Class groups for integral representations of metacyclic groups, Mathematika 19 (1972), 105–111.

    Article  MathSciNet  MATH  Google Scholar 

  13. M. Kervaire, M.P. Murthy, On the projective class group of cyclic groups of prime power order, Comment. Math. Helv. 52 (1977), 415–452.

    Article  MathSciNet  MATH  Google Scholar 

  14. T.-Y. Lam, Induction theorems for Grothendieck groups and Whitehead groups of finite groups, Ann. Sci. Ec. Norm. Sup. 1 (1968), 91–148.

    MathSciNet  MATH  Google Scholar 

  15. T.-Y. Lam, Artin exponent of finite groups, J. Alg. 9 (1968), 94–119.

    Article  MathSciNet  MATH  Google Scholar 

  16. A. Matchett, Class groups of cyclic groups of square free orders, Trans. Amer. Math. Soc. 264 (1981), 251–254.

    MathSciNet  MATH  Google Scholar 

  17. J. Milgram, Odd index subgroups of units in cyclotomic fields and applications, Lecture Notes in Math. 854, Springer-Verlag (1981), 269–298.

    Google Scholar 

  18. J. Milnor, Introduction to algebraic K-theory, Princeton Univ. Press (1971).

    Google Scholar 

  19. G. Mislin, The finiteness obstructions for nilpotent spaces lie in D(ZG), Invent. math. 53 (1979), 185–191.

    Article  MathSciNet  MATH  Google Scholar 

  20. R. Oliver, Group actions on disks, integral permutation representations, and the Burnside ring, Proc. Symp. Pure Math. 32 (1978), 339–346.

    Article  MathSciNet  Google Scholar 

  21. R. Oliver, G-actions on disks and permutation representations II, Math. Z. 157 (1977), 237–263.

    Article  MathSciNet  MATH  Google Scholar 

  22. R. Oliver, Subgroups generating D(ZG), J. Alg. 55 (1978), 43–57.

    Article  MathSciNet  MATH  Google Scholar 

  23. R. Oliver, SK1 for finite group rings II, Math. Scand. 47 (1980), 195–231.

    MathSciNet  MATH  Google Scholar 

  24. R. Oliver, Class groups of cyclic p-groups, Mathematika 30 (1983), 26–57.

    Article  MathSciNet  MATH  Google Scholar 

  25. R. Oliver, D(ZG)+ and the Artin cokernal, Comment. Math. Helv. 58 (1983), 291–311.

    Article  MathSciNet  Google Scholar 

  26. R. Oliver, The Whitehead transfer homomorphism for oriented S1-bundles, Math. Scand. (to appear).

    Google Scholar 

  27. R. Oliver, L. Taylor, Logarithmic descriptions of Whitehead groups and class groups for p-groups (to appear).

    Google Scholar 

  28. I. Reiner, Projective class groups of symmetric and alternating groups, Lin. and Multilin. Alg. 3 (1975), 147–153.

    Article  MathSciNet  MATH  Google Scholar 

  29. I. Reiner, Maximal orders, Acad. Press (1975).

    Google Scholar 

  30. D.S. Rim, Modules over finite groups, Ann. Math. 69 (1969), 700–712.

    Article  MathSciNet  MATH  Google Scholar 

  31. P. Roquette, Realizierung von Darstellungen endlicher nilpotenter Gruppen, Arkiv der Math. 9 (1958), 241–250.

    MathSciNet  MATH  Google Scholar 

  32. R. Swan, Induced representations and projective modules, Ann. Math. 71 (1960), 552–578.

    Article  MathSciNet  MATH  Google Scholar 

  33. R. Swan, Periodic resolutions of finite groups, Ann. Math. 72 (1960), 267–291.

    Article  MathSciNet  MATH  Google Scholar 

  34. M. Taylor, Locally free classgroups of groups of prime power order, J. Algebra 50 (1978), 463–487.

    Article  MathSciNet  MATH  Google Scholar 

  35. M. Taylor, The locally free classgroup of the symmetric group, Ill. J. Math. 23 (1979), 687–702.

    MathSciNet  MATH  Google Scholar 

  36. M. Taylor, A logarithmic approach to classgroups of integral group rings, J. Alg. 66 (1980), 321–353.

    Article  MathSciNet  MATH  Google Scholar 

  37. M. Taylor, On Fröhlich’s conjecture for rings of integers of tame extensions, Invent. math. 63 (1981), 41–79.

    Article  MathSciNet  MATH  Google Scholar 

  38. S. Ullom, A note on the classgroup of integral group rings of some cyclic groups, Mathematika 17 (1970), 79–81.

    Article  MathSciNet  MATH  Google Scholar 

  39. S. Ullom, The exponent of class groups, J. Alg. 29 (1974), 124–132.

    Article  MathSciNet  MATH  Google Scholar 

  40. S. Ullom, Nontrivial lower bounds for class groups of integral group rings, Ill. J. Math. 20 (1976), 361–371.

    MathSciNet  MATH  Google Scholar 

  41. S. Ullom, A survey of class groups of integral group rings, Algebraic number fields, Acad. Press (1977), 497–524.

    Google Scholar 

  42. S. Ullom, Fine structure of class groups of cyclic p-groups, J. Alg. 49 (1977), 112–124.

    Article  MathSciNet  MATH  Google Scholar 

  43. S. Ullom, Class groups of cyclotomic fields and group rings, J. London Math. Soc. 17 (1978), 231–239.

    Article  MathSciNet  MATH  Google Scholar 

  44. C.T.C. Wall, Norms of units in group rings, Proc. London Math. Soc. 29 (1974), 593–632.

    Article  MathSciNet  MATH  Google Scholar 

  45. A. Weil, Basic number theory, Springer-Verlag (1967).

    Google Scholar 

Download references

Authors
  1. Robert Oliver
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Irving Reiner Klaus W. Roggenkamp

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Oliver, R. (1985). Projective class groups of integral group rings: a survey. In: Reiner, I., Roggenkamp, K.W. (eds) Orders and their Applications. Lecture Notes in Mathematics, vol 1142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074803

Download citation

  • DOI: https://doi.org/10.1007/BFb0074803

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15674-1

  • Online ISBN: 978-3-540-39601-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation