A note on olsson's conjecture

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Authors

  • Lászlo Héthelyi
  • Burkhard Külshammer
  • Benjamin Sambale

External Research Organisations

  • Budapest University of Technology and Economics
  • Friedrich Schiller University Jena
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Details

Original languageEnglish
Pages (from-to)364-385
Number of pages22
JournalJournal of algebra
Volume398
Publication statusPublished - 15 Jan 2014
Externally publishedYes

Abstract

For a p-block B of a finite group G with defect group D Olsson conjectured that k0(B) ≤ |D : D '|, where k0(B) is the number of characters in B of height 0 and D ' denotes the commutator subgroup of D. Brauer deduced Olsson's Conjecture in the case where D is a dihedral 2-group using the fact that certain algebraically conjugate subsections are also conjugate in G. We generalize Brauer's argument for arbitrary primes p and arbitrary defect groups. This extends two results by Robinson. For p > 3 we show that Olsson's Conjecture is satisfied for defect groups of p-rank 2 and for minimal non-abelian defect groups.

Keywords

    Block, Characters, Defect group, Height, P-Rank, Subsection

ASJC Scopus subject areas

Cite this

A note on olsson's conjecture. / Héthelyi, Lászlo; Külshammer, Burkhard; Sambale, Benjamin.
In: Journal of algebra, Vol. 398, 15.01.2014, p. 364-385.

Research output: Contribution to journal › Article › Research › peer review

Héthelyi, L, Külshammer, B & Sambale, B 2014, 'A note on olsson's conjecture', Journal of algebra, vol. 398, pp. 364-385. https://doi.org/10.1016/j.jalgebra.2012.08.010
Héthelyi, L., Külshammer, B., & Sambale, B. (2014). A note on olsson's conjecture. Journal of algebra, 398, 364-385. https://doi.org/10.1016/j.jalgebra.2012.08.010
Héthelyi L, Külshammer B, Sambale B. A note on olsson's conjecture. Journal of algebra. 2014 Jan 15;398:364-385. doi: 10.1016/j.jalgebra.2012.08.010
Héthelyi, Lászlo ; Külshammer, Burkhard ; Sambale, Benjamin. / A note on olsson's conjecture. In: Journal of algebra. 2014 ; Vol. 398. pp. 364-385.
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AU - Külshammer, Burkhard

AU - Sambale, Benjamin

N1 - Funding Information: The first author was supported by an OTKA Grant (National Scientific Research Grant No. 77-476). The third author is supported by the “Deutsche Forschungsgemeinschaft”. We are grateful to the referee for some valuable comments.

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