The Brauer Indecomposability of Scott Modules for the Quadratic Group Qd(p)

Let k be an algebraically closed field of prime characteristic p and P a finite p -group. We compute the Scott k G -module with vertex P when F is a constrained fusion system on P and G is Park’s group for F . In the case that F is a fusion system of the quadratic group Qd ( p ) = ( Z / p × Z / p )...

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Bibliographic Details
Published inAlgebras and representation theory Vol. 22; no. 6; pp. 1387 - 1397
Main Authors Koshitani, Shigeo, Tuvay, İpek
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2019
Springer Nature B.V
Subjects
Associative Rings and Algebras
Commutative Rings and Algebras
Mathematics
Mathematics and Statistics
Modules
Non-associative Rings and Algebras
Subgroups
Scott module
The quadratic group
20C20
Constrained fusion system
20C05
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Summary:Let k be an algebraically closed field of prime characteristic p and P a finite p -group. We compute the Scott k G -module with vertex P when F is a constrained fusion system on P and G is Park’s group for F . In the case that F is a fusion system of the quadratic group Qd ( p ) = ( Z / p × Z / p ) ? SL ( 2 , p ) on a Sylow p -subgroup P of Qd( p ) and G is Park’s group for F , we prove that the Scott k G -module with vertex P is Brauer indecomposable.
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-018-9825-1