The inductive blockwise Alperin weight condition for certain 2-blocks with abelian defect groups

2021 ◽  
Vol 579 ◽  
pp. 174-194
Author(s):  
Kun Zhang ◽  
Yuanyang Zhou
Keyword(s):  
Defect Groups ◽  
Weight Condition ◽  
Abelian Defect Groups

scholarly journals SIMPLE MODULES IN THE AUSLANDER–REITEN QUIVER OF PRINCIPAL BLOCKS WITH ABELIAN DEFECT GROUPS

2018 ◽  
Vol 235 ◽  
pp. 58-85
Author(s):  
SHIGEO KOSHITANI ◽  
CAROLINE LASSUEUR
Keyword(s):  
Finite Group ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Simple Modules ◽  
Principal Block ◽  
Defect Groups ◽  
Abelian Defect Groups ◽  
A Finite Group

Given an odd prime $p$ , we investigate the position of simple modules in the stable Auslander–Reiten quiver of the principal block of a finite group with noncyclic abelian Sylow $p$ -subgroups. In particular, we prove a reduction to finite simple groups. In the case that the characteristic is $3$ , we prove that simple modules in the principal block all lie at the end of their components.

On Blocks with Abelian Defect Groups of Small Rank

2016 ◽  
Vol 71 (1-2) ◽  
pp. 411-422 ◽  
Author(s):  
Benjamin Sambale
Keyword(s):  
Small Rank ◽  
Defect Groups ◽  
Abelian Defect Groups

scholarly journals Donovan’s conjecture and blocks with abelian defect groups

2018 ◽  
Vol 147 (3) ◽  
pp. 963-970 ◽  
Author(s):  
Charles W. Eaton ◽  
Michael Livesey
Keyword(s):  
Defect Groups ◽  
Abelian Defect Groups

scholarly journals Schur indices and abelian defect groups

2008 ◽  
Vol 319 (10) ◽  
pp. 4140-4146 ◽  
Author(s):  
Michael Geline
Keyword(s):  
Defect Groups ◽  
Abelian Defect Groups

scholarly journals Loewy lengths of blocks with abelian defect groups

2017 ◽  
Vol 4 (3) ◽  
pp. 21-30 ◽  
Author(s):  
Charles W. Eaton ◽  
Michael Livesey
Keyword(s):  
Defect Groups ◽  
Abelian Defect Groups
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