Towards Donovan's conjecture for abelian defect groups

Charles W. Eaton; Michael Livesey

doi:10.1016/j.jalgebra.2018.09.043

Towards Donovan's conjecture for abelian defect groups

Charles W. Eaton
, Michael Livesey^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We define a new invariant for a p-block of a finite group, the strong Frobenius number, which we use to address the problem of reducing Donovan's conjecture to normal subgroups of index p. As an application we use the strong Frobenius number to complete the proof of Donovan's conjecture for 2-blocks with abelian defect groups of rank at most 4 and for 2-blocks with abelian defect groups of order at most 64.

Original language	English
Pages (from-to)	39-61
Number of pages	23
Journal	Journal of Algebra
Volume	519
Early online date	5 Nov 2018
DOIs	https://doi.org/10.1016/j.jalgebra.2018.09.043
Publication status	Published - 1 Feb 2019

Keywords

Abelian defect groups
Donovan's conjecture
Finite groups
Modular representation theory

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10.1016/j.jalgebra.2018.09.043

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title = "Towards Donovan's conjecture for abelian defect groups",

abstract = "We define a new invariant for a p-block of a finite group, the strong Frobenius number, which we use to address the problem of reducing Donovan's conjecture to normal subgroups of index p. As an application we use the strong Frobenius number to complete the proof of Donovan's conjecture for 2-blocks with abelian defect groups of rank at most 4 and for 2-blocks with abelian defect groups of order at most 64.",

keywords = "Abelian defect groups, Donovan's conjecture, Finite groups, Modular representation theory",

author = "Eaton, \{Charles W.\} and Michael Livesey",

year = "2019",

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doi = "10.1016/j.jalgebra.2018.09.043",

language = "English",

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journal = "Journal of Algebra",

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AU - Eaton, Charles W.

AU - Livesey, Michael

PY - 2019/2/1

Y1 - 2019/2/1

N2 - We define a new invariant for a p-block of a finite group, the strong Frobenius number, which we use to address the problem of reducing Donovan's conjecture to normal subgroups of index p. As an application we use the strong Frobenius number to complete the proof of Donovan's conjecture for 2-blocks with abelian defect groups of rank at most 4 and for 2-blocks with abelian defect groups of order at most 64.

AB - We define a new invariant for a p-block of a finite group, the strong Frobenius number, which we use to address the problem of reducing Donovan's conjecture to normal subgroups of index p. As an application we use the strong Frobenius number to complete the proof of Donovan's conjecture for 2-blocks with abelian defect groups of rank at most 4 and for 2-blocks with abelian defect groups of order at most 64.

KW - Abelian defect groups

KW - Donovan's conjecture

KW - Finite groups

KW - Modular representation theory

UR - https://www.scopus.com/pages/publications/85056169243

U2 - 10.1016/j.jalgebra.2018.09.043

DO - 10.1016/j.jalgebra.2018.09.043

M3 - Article

AN - SCOPUS:85056169243

SN - 0021-8693

VL - 519

SP - 39

EP - 61

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Towards Donovan's conjecture for abelian defect groups

Abstract

Keywords

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