2-Blocks whose defect group is homocyclic and whose inertial quotient contains a Singer cycle

JOURNAL OF ALGEBRA

卷:563

Article

McKernon, Elliot¹ 

[1] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

关键词: Block theory;    Modular representation theory, finite groups;    Donovan's conjecture;    Singer cycles;    Morita equivalence;   

DOI  :  10.1016/j.jalgebra.2020.06.029

来源: Elsevier

【 摘 要 】

We consider a block B of a finite group with defect group D congruent to (C-2m)(n) and inertial quotient E containing a Singer cycle (an element of order 2(n) - 1). This implies E = E (sic) F, where E congruent to C-2n(-1), F <= C-n, and E acts transitively on the elements in D of order 2. We classify the basic Morita equivalence classes of B over a complete discrete valuation ring O: when m = 1, B is basic Morita equivalent to the principal block of one of SL2(2(n)) (sic) F, D (sic) E, or J(1) (where J(1) occurs only when n = 3). When m > 1, B is basic Morita equivalent to D (sic) E. Crown Copyright (C) 2020 Published by Elsevier Inc. All rights reserved.

【 授权许可】

Free