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- Title
BLOCKS WITH NORMAL ABELIAN DEFECT AND ABELIAN p′ INERTIAL QUOTIENT.
- Authors
Benson, David; Kessar, Radha; Linckelmann, Markus
- Abstract
Let |$k$| be an algebraically closed field of characteristic |$p$| , and let |${\mathcal{O}}$| be either |$k$| or its ring of Witt vectors |$W(k)$|. Let |$G$| be a finite group and |$B$| a block of |${\mathcal{O}} G$| with normal abelian defect group and abelian |$p^{\prime}$| inertial quotient |$L$|. We show that |$B$| is isomorphic to its second Frobenius twist. This is motivated by the fact that bounding Frobenius numbers is one of the key steps towards Donovan's conjecture. For |${\mathcal{O}}=k$| , we give an explicit description of the basic algebra of |$B$| as a quiver with relations. It is a quantized version of the group algebra of the semidirect product |$P\rtimes L$|.
- Subjects
ABELIAN groups; FINITE groups; ALGEBRA; GROUP algebras
- Publication
Quarterly Journal of Mathematics, 2019, Vol 70, Issue 4, p1437
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmathj/haz025