Skip to main content
SpringerLink
Log in

Research in Representation Theory at Mainz (1984–1990)

  • Chapter
Representation Theory of Finite Groups and Finite-Dimensional Algebras

Part of the book series: Progress in Mathematics ((PM,volume 95))

Abstract

This is a report on research conducted at Mainz from 1984 to 1990, made possible by the DFG-project.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover 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. T. Berger, “Characters and derived lengths in groups of odd order”, Journal of Algebra 39 (1976), 199–207.

    Article  MathSciNet  MATH  Google Scholar 

  2. F. Bernhardt, “Modular character degrees and the structure of solvable groups”, to appear Arch. Math.

    Google Scholar 

  3. F. Bernhardt, “On p-groups with three orbit sizes”, to appear.

    Google Scholar 

  4. F. Bernhardt, P. Landrock, O. Manz, “The extended Golay codes considered as ideals”, Aarhus Preprint Series 1988/89 No.3.

    Google Scholar 

  5. W. Burnside, “On soluble irreducible groups of linear substitutions substitutions in a prime number of variables”, Acta mathematica 27 (1903), 217–224.

    Article  MathSciNet  MATH  Google Scholar 

  6. D. Chillag, M. Herzog, “On the lengths of the conjugacy classes of finite groups”, J. of Algebra 131 (1990), 110–125.

    Article  MathSciNet  MATH  Google Scholar 

  7. A.K. Feyzioglu, “Charaktergrade und die Kommutatorlänge in auflösbaren Gruppen”, J. Algebra 126, no.l (1989), 225–251.

    Article  MathSciNet  MATH  Google Scholar 

  8. D. Gluck, “Bounding the number of character degrees of a solvable group”, Journal of the London Mathematical Society. Vol. 31 (1984), 457–462.

    Article  MathSciNet  Google Scholar 

  9. D. Gluck, “A conjecture about character degrees of solvable groups”.

    Google Scholar 

  10. D. Gluck, O. Manz, “Prime factors of character degrees and group structure”, Proc. of Symposia in Pure Math. 47, Vol. II (1987), 65–69.

    Google Scholar 

  11. R. Gow, B. Huppert, “Degree problems of representation theory over arbitrary fields of characteristic 0, Part 0: On theorems of N. Itô and J.G. Thompson, J. reine angew. Math. 381 (1987), 136–147.

    MathSciNet  MATH  Google Scholar 

  12. R. Gow, B. Huppert, “Degree problems of representation theory over arbitrary fields of characteristic 0, Part 2: Groups which have only two reduced degrees, J. reine angew. Math. 389 (1988), 122–132.

    MathSciNet  MATH  Google Scholar 

  13. T. Hawkes, “Groups with isomorphic complex group algebras”, to appear.

    Google Scholar 

  14. B. Huppert, “A characterization of GL(2,3) and SL(2,5) by the degrees of their representations”, Forum Mathematicum 1 (1989), 167–183.

    Article  MathSciNet  MATH  Google Scholar 

  15. B. Huppert, “Inequalities for character degrees of solvable groups”, Arch. Math., Vol.46 (1986), 387–392.

    Article  MathSciNet  MATH  Google Scholar 

  16. B. Huppert, “Solvable groups, all of whose irreducible representations in characteristic p have prime degrees”, J. of Algebra, Vol. 104, No.1, 23–36.

    Google Scholar 

  17. B. Huppert, O. Manz, “Non solvable groups, whose character degrees are degrees are products of at most two prime numbers”, Osaka J. Math. 23 (1986), 491–502.

    MathSciNet  MATH  Google Scholar 

  18. B. Huppert, O. Manz, “Degree-problems I. Square free character degrees”, Arch. Math., Vol. 45 (1985), 125–132.

    Article  MathSciNet  MATH  Google Scholar 

  19. B. Huppert, O. Manz, “Orbit sizes of p-groups”, Arch. Math. 54 (1990), 105–110.

    Article  MathSciNet  MATH  Google Scholar 

  20. I.M. Isaacs, “Recovering information about a group from its complex algebra”, Arch. Math. Vol. 47 (1986), 293–295.

    Article  MathSciNet  MATH  Google Scholar 

  21. I.M. Isaacs, “Sets of p-powers as irreducible character degrees”, Proc. Am. Math. Soc. Vol. 96, no.4.

    Google Scholar 

  22. I.M. Isaacs, “Lengths and numbers of modular character degrees for solvable groups”, to appear.

    Google Scholar 

  23. I.M. Isaacs, “Coprime group actions fixing all nonlinear irreducible characters”, Can. J. Math. Vol. XL, No.1 (1989), 68–82.

    Article  MathSciNet  Google Scholar 

  24. I.M. Isaacs, “Groups having at most three irreducible character degrees”, Proc. Amer. Math. Soc. 21 (1969), 185–188.

    Article  MathSciNet  MATH  Google Scholar 

  25. I.M. Isaacs, D. Passman, “A characterization of groups in terms of the degrees of their characters II”, Pacific Journal of Mathematics Vol. 24, No.3, 1968.

    Google Scholar 

  26. N. Itô “On the degrees of irreducible representations of a finite group”, Nagoya Math. J. 3 (1951), 5–6.

    MathSciNet  MATH  Google Scholar 

  27. N. Itô, “Some studies of group characters”, Nagoya Math. J. 2 (1951), 17–28.

    MathSciNet  MATH  Google Scholar 

  28. R. Knörr, W. Willems, “The automorphism groups of generalized Reed Muller codes”, to appear in Asterisque.

    Google Scholar 

  29. R. Knörr, W. Willems, “A characterization of generalized Reed Muller codes”, Preprint.

    Google Scholar 

  30. P. Landrock, O. Manz, “Classical codes as ideals in group algebras”, Aarhus Preprint Series 1986/87, No. 18.

    Google Scholar 

  31. C.R. Leedham-Green, R. Staszewski, “On the Loewy and Jennings series of a finite p-group”, to appear.

    Google Scholar 

  32. U. Leisering, “Ordinary and p-modular character degrees of prime power”, to appear in Arch. Math., Vol. 53.

    Google Scholar 

  33. U. Leisering, O. Manz, “A note on character degrees of solvable groups”, Arch. Math., Vol. 48 (1987), 32–35.

    Article  MathSciNet  MATH  Google Scholar 

  34. O. Manz, “Endliche auflösbare Gruppen, deren sämtliche Charaktergrade Primzahlpotenzen sind”, J. of Algebra, Vol. 94 No. 1, (1985).

    Google Scholar 

  35. O. Manz, “Endliche nicht-auflösbare Gruppen, deren sämtliche Charaktergrade Primzahlpotenzen sind”, J. of Algebra, Vol. 96, No.1, (1985), 114–119.

    Article  MathSciNet  MATH  Google Scholar 

  36. O. Manz, U. Stammbach, R. Staszewski, “On the Loewy-series of the group algebra of groups of small p-length”, Comm. in Algebra 17 (1989), 1249–1274.

    Article  MathSciNet  MATH  Google Scholar 

  37. O. Manz, R. Staszewski, “On the Loewy-series of the modular group algebra of a finite p-group”, J. reine angewandte Math. 368 (1986), 108–118.

    MathSciNet  MATH  Google Scholar 

  38. O. Manz, R. Staszewski, W. Willems, “On the number of components of a graph related to character degrees”, Proc. Amer. Math. Soc. 103 (1988), 31–37.

    Article  MathSciNet  MATH  Google Scholar 

  39. O. Manz, W. Willems, T. Wolf, “The diameter of the character degree graph”, J. reine angew. Math. 402 (1989), 181–198.

    MathSciNet  MATH  Google Scholar 

  40. O. Manz, T. Wolf, “Brauer characters of q′-degrees in p-solvable groups”, J. of Algebra, Vol. 115, No.1 (1988), 75–91.

    Article  MathSciNet  MATH  Google Scholar 

  41. G. Michler, “A finite simple group of Lie-type has p-block with different defects, p ≠ 2”, J. of Algebra 104 (1986), 220–230.

    Article  MathSciNet  MATH  Google Scholar 

  42. G. Navarro, “Two groups with isomorphic group algebras”, to appear in Arch. Math.

    Google Scholar 

  43. T. Okuyama, “On a problem of Wallace”, to appear.

    Google Scholar 

  44. H. Pahlings, “Character degrees and normal p-complements”, Comm. in Algebra 3(1) (1975), 75–80.

    Article  MathSciNet  MATH  Google Scholar 

  45. U. Stammbach, M. Stricker, “A remark on the Loewy-layers of the modular group ring of a finite p-group”, Topology Appl. 25 (1987), 121–124.

    Article  MathSciNet  Google Scholar 

  46. K. Taketa, “Über die Gruppen, deren Darstellungen sich sämtlich auf monomiale Gestalt transformieren lassen”, Proc. Acad. Tokyo 6 (1930), 31–33.

    Article  MathSciNet  MATH  Google Scholar 

  47. J.G. Thompson, “Normal p-complements and irreducible characters”, J. of Algebra 14 (1970), 129–134.

    Article  MATH  Google Scholar 

  48. W. Willems, “Blocks of defect zero in finite simple groups”, J. of Algebra 113 (1988), 511–522.

    Article  MathSciNet  MATH  Google Scholar 

  49. W. Willems, “An upper bound for Loewy-lengths of projective modules in p-solvable groups”, Osaka J. Math. 24 (1987), 471–478.

    MathSciNet  Google Scholar 

Download references

Authors
  1. Bertram Huppert
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Experimentelle Mathematik, Universität GHS Essen, Ellernstrasse 29, D-4300, Essen 12, Germany

    G. O. Michler

  2. Fakultät für Mathematik, Universität Bielefeld, Universitätsstrasse, D-4800, Bielefeld, Germany

    C. M. Ringel

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Basel AG

About this chapter

Cite this chapter

Huppert, B. (1991). Research in Representation Theory at Mainz (1984–1990). In: Michler, G.O., Ringel, C.M. (eds) Representation Theory of Finite Groups and Finite-Dimensional Algebras. Progress in Mathematics, vol 95. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8658-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8658-1_2

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9720-4

  • Online ISBN: 978-3-0348-8658-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation