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Proceedings of the Second International Conference on the Theory of Groups pp 103–130Cite as

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On the Structure of Blocks of Characters of Finite Groups

On the Structure of Blocks of Characters of Finite Groups

  • Richard Brauer2 
  • Conference paper
  • 1298 Accesses

  • 4 Citations

Part of the Lecture Notes in Mathematics book series (LNM,volume 372)

Abstract

The role played by characters in recent work on finite groups can be described as follows. Given rather incomplete information concerning a finite group G, we try to find the table of irreducible characters of G. If we succeed, we use the character table of G to obtain additional information on G. We may also try a similar procedure in order to show that finite groups with certain given properties do not exist.

Keywords

  • Finite Group
  • Conjugacy Class
  • Irreducible Character
  • Primitive Element
  • Double Coset

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Richard Brauer, “Zur Darstellungstheorie der Gruppen endlicher Ordnung”, Math. Z. 63 (1955/56), 406–444. MR17,824.

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  2. Richard Brauer, “Zur Darstellungstheorie der Gruppen endlicher Ordnung. II”, Math. Z. 72 (1959), 25–46. MR21#7258.

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  3. Richard Brauer, “On blocks and sections in finite groups. I”, Amer. J. Math. 89 (1967), 1115–1136. MR36#2716.

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  4. Richard Brauer, “On blocks and sections in finite groups, II”, Amer. J. Math. 90 (1968), 895–925. MR39#5713.

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  5. Charles W. Curtis, Irving Reiner, Representation theory of finite groups and associative algebras, (Pure and Appl. Math., 11. Interscience [John Wiley & Sons], New York, London, 1962). MR26#2519.

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  6. Larry Dornhoff, Group representation theory, Part B: Modular representation theory,(Pure and Appl. Math., 7. Marcel Dekker, New York, 1972). Zbl. 236.20004.

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  7. P. Fong, “On the characters of p-solvable groups”, Trans. Amer. Math. Soc. 98 (1961), 263–284. MR22#11052.

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Author information

Authors and Affiliations

  1. Harvard University, Cambridge, USA

    Richard Brauer

Authors
  1. Richard Brauer
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics, Institute of Advanced Studies, Australian National University, 2600, Canberra, ACT, Australia

    M. F. Newman

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© 1974 Springer-Verlag Berlin Heidelberg

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Brauer, R. (1974). On the Structure of Blocks of Characters of Finite Groups. In: Newman, M.F. (eds) Proceedings of the Second International Conference on the Theory of Groups. Lecture Notes in Mathematics, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21571-5_9

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  • DOI: https://doi.org/10.1007/978-3-662-21571-5_9

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  • Print ISBN: 978-3-540-06845-7

  • Online ISBN: 978-3-662-21571-5

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