Blocks with defect group Q2n × C2m and SD 2n × C2m

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Authors

  • Benjamin Sambale

External Research Organisations

  • Friedrich Schiller University Jena
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Details

Original languageEnglish
Pages (from-to)1717-1732
Number of pages16
JournalAlgebras and representation theory
Volume16
Issue number6
Publication statusPublished - Dec 2013
Externally publishedYes

Abstract

We determine the numerical invariants of blocks with defect group Q 2n × C2m and SD2n × C2m, where Q2n denotes a quaternion group of order 2n, C2m denotes a cyclic group of order 2m, and SD2n denotes a semidihedral group of order 2n. This generalizes Olsson's results for m = 0. As a consequence, we prove Brauer's k(B)- Conjecture, Olsson's Conjecture, Brauer's Height-Zero Conjecture, the Alperin- McKay Conjecture, Alperin's Weight Conjecture and Robinson's Ordinary Weight Conjecture for these blocks.Moreover, we show that the gluing problem has a unique solution in this case. This paper follows (and uses) (Sambale, J Pure Appl Algebra 216:119-125, 2012; Proc Amer Math Soc, 2012).

Keywords

    2-blocks, Alperin'sWeight Conjecture, Ordinary weight conjecture, Quaternion defect groups, Semidihedral defect groups

ASJC Scopus subject areas

Cite this

Blocks with defect group Q2n × C2m and SD 2n × C2m. / Sambale, Benjamin.
In: Algebras and representation theory, Vol. 16, No. 6, 12.2013, p. 1717-1732.

Research output: Contribution to journalArticleResearchpeer review

Sambale B. Blocks with defect group Q2n × C2m and SD 2n × C2m. Algebras and representation theory. 2013 Dec;16(6):1717-1732. doi: 10.1007/s10468-012-9379-6
Sambale, Benjamin. / Blocks with defect group Q2n × C2m and SD 2n × C2m. In: Algebras and representation theory. 2013 ; Vol. 16, No. 6. pp. 1717-1732.
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AU - Sambale, Benjamin

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N2 - We determine the numerical invariants of blocks with defect group Q 2n × C2m and SD2n × C2m, where Q2n denotes a quaternion group of order 2n, C2m denotes a cyclic group of order 2m, and SD2n denotes a semidihedral group of order 2n. This generalizes Olsson's results for m = 0. As a consequence, we prove Brauer's k(B)- Conjecture, Olsson's Conjecture, Brauer's Height-Zero Conjecture, the Alperin- McKay Conjecture, Alperin's Weight Conjecture and Robinson's Ordinary Weight Conjecture for these blocks.Moreover, we show that the gluing problem has a unique solution in this case. This paper follows (and uses) (Sambale, J Pure Appl Algebra 216:119-125, 2012; Proc Amer Math Soc, 2012).

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