Proceedings of the Japan Academy, Series A, Mathematical Sciences

On Brauer’s height zero conjecture

Masafumi Murai

Full-text: Open access

Abstract

We give a reduction theorem for Brauer’s height zero conjecture.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci. Volume 88, Number 3 (2012), 38-40.

Dates
First available in Project Euclid: 5 March 2012

Permanent link to this document
http://projecteuclid.org/euclid.pja/1330958574

Digital Object Identifier
doi:10.3792/pjaa.88.38

Zentralblatt MATH identifier
0848.20005

Mathematical Reviews number (MathSciNet)
MR2908621

Subjects
Primary: 20C20: Modular representations and characters

Keywords
Brauer’s height zero conjecture

Citation

Murai, Masafumi. On Brauer’s height zero conjecture. Proceedings of the Japan Academy, Series A, Mathematical Sciences 88 (2012), no. 3, 38--40. doi:10.3792/pjaa.88.38. http://projecteuclid.org/euclid.pja/1330958574.


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References

  • T. R. Berger and R. Knörr, On Brauer's height 0 conjecture, Nagoya Math. J. 109 (1988), 109–116.
  • E. C. Dade, Counting characters in blocks, II, J. Reine Angew. Math. 448 (1994), 97–190.
  • D. Gluck and T. R. Wolf, Brauer's height conjecture for $p$-solvable groups, Trans. Amer. Math. Soc. 282 (1984), no. 1, 137–152.
  • B. Külshammer and L. Puig, Extensions of nilpotent blocks, Invent. Math. 102 (1990), no. 1, 17–71.
  • M. Murai, Block induction, normal subgroups and characters of height zero, Osaka J. Math. 31 (1994), no. 1, 9–25.
  • M. Murai, A remark on Brauer's height zero conjecture, J. Math. Kyoto Univ. 35 (1995), no. 4, 607–610.
  • M. Murai, Normal subgroups and heights of characters, J. Math. Kyoto Univ. 36 (1996), no. 1, 31–43.
  • H. Nagao and Y. Tsushima, Representations of finite groups, Academic Press, New York, 1989.
  • G. Navarro and P. H. Tiep, Brauer's height zero conjecture for the 2-blocks of maximal defect. (to appear in J. Reine Angew. Math.).
  • G. R. Robinson, Cancellation theorems related to conjectures of Alperin and Dade, J. Algebra 249 (2002), no. 1, 196–219.