Brauer's height zero conjecture for metacyclic defect groups

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Authors

  • Benjamin Sambale

External Research Organisations

  • Friedrich Schiller University Jena
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Details

Original languageEnglish
Pages (from-to)481-507
Number of pages27
JournalPacific journal of mathematics
Volume262
Issue number2
Publication statusPublished - 2013
Externally publishedYes

Abstract

We prove that Brauer's height zero conjecture holds for p-blocks of finite groups with metacyclic defect groups. If the defect group is nonabelian and contains a cyclic maximal subgroup, we obtain the distribution into p-conjugate and p-rational irreducible characters. The Alperin-McKay conjecture then follows provided p = 3. Along the way we verify a few other conjectures. Finally we consider more closely the extraspecial defect group of order p3 and exponent p2 for an odd prime. Here for blocks with inertial index 2 we prove the Galois-Alperin-McKay conjecture by computing k0.B/. Then for p ≤ 11 also Alperin's weight conjecture follows. This improves results of Gao (2012), Holloway, Koshitani, Kunugi (2010) and Hendren (2005).

Keywords

    Alperin's weight conjecture, Brauer's height zero conjecture, Metacyclic defect groups

ASJC Scopus subject areas

Cite this

Brauer's height zero conjecture for metacyclic defect groups. / Sambale, Benjamin.
In: Pacific journal of mathematics, Vol. 262, No. 2, 2013, p. 481-507.

Research output: Contribution to journalArticleResearchpeer review

Sambale B. Brauer's height zero conjecture for metacyclic defect groups. Pacific journal of mathematics. 2013;262(2):481-507. doi: 10.2140/pjm.2013.262.481
Sambale, Benjamin. / Brauer's height zero conjecture for metacyclic defect groups. In: Pacific journal of mathematics. 2013 ; Vol. 262, No. 2. pp. 481-507.
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