Towards Donovan's conjecture for abelian defect groups

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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.

Bibliographical metadata

Original languageEnglish
Pages (from-to)39-61
Number of pages23
JournalJournal of Algebra
Early online date5 Nov 2018
Publication statusPublished - 1 Feb 2019