Blocks with cyclic hyperfocal subgroups

In this paper, we investigate the block with a cyclic hyperfocal subgroup and abelian quotient group of a defect group with respect to this hyperfocal subgroup. First, in the light of Rouquier's conjecture, we get an isotypy between the block and its Brauer correspondent in the normalizer of th...

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Bibliographic Details
Published inJournal of algebra Vol. 609; pp. 734 - 763
Main Authors Hu, Xueqin, Zhou, Yuanyang
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.11.2022
Subjects
Hyperfocal subalgebras
Hyperfocal subgroups
Isotypies
Rouquier's conjecture
Hyperfocal subgroups
Hyperfocal subalgebras
Rouquier's conjecture
Isotypies
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Summary:In this paper, we investigate the block with a cyclic hyperfocal subgroup and abelian quotient group of a defect group with respect to this hyperfocal subgroup. First, in the light of Rouquier's conjecture, we get an isotypy between the block and its Brauer correspondent in the normalizer of the defect group. Second, we verify the ‘if part’ of a conjecture proposed by Kessar, Linckelmann and Navarro, which can be viewed as the ‘hyperfocal’ version of Brauer's height zero conjecture. Moreover, we obtain the number of irreducible characters of the hyperfocal subalgebra of the block considered here.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2022.06.035