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Blocks with normal abelian defect and abelian p′ inertial quotient

Benson, D., Kessar, R. ORCID: 0000-0002-1893-4237 and Linckelmann, M. (2019). Blocks with normal abelian defect and abelian p′ inertial quotient. The Quarterly Journal of Mathematics, 70(4), pp. 1437-1448. doi: 10.1093/qmathj/haz025

Abstract

Let k be an algebraically closed field of characteristic p⁠, and let O be either k or its ring of Witt vectors W(k)⁠. Let G be a finite group and B a block of OG with normal abelian defect group and abelian p′ 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 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⋊L⁠.

Publication Type: Article
Additional Information: This is a pre-copyedited, author-produced version of an article accepted for publication in Quarterly Journal of Mathematics following peer review. The version of record David Benson, Radha Kessar, Markus Linckelmann, BLOCKS WITH NORMAL ABELIAN DEFECT AND ABELIAN p′ INERTIAL QUOTIENT, The Quarterly Journal of Mathematics, Volume 70, Issue 4, December 2019, Pages 1437–1448, is available online at: https://doi.org/10.1093/qmathj/haz025
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: https://openaccess.city.ac.uk/id/eprint/23737
[img] Text - Accepted Version
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