Rationality of blocks of quasi-simple finite groups

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autorschaft

  • Niamh Farrell
  • Radha Kessar

Externe Organisationen

  • Technische Universität Kaiserslautern
  • University of London
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Details

OriginalspracheEnglisch
Seiten (von - bis)325-349
Seitenumfang25
FachzeitschriftRepresentation Theory
Jahrgang23
Ausgabenummer11
PublikationsstatusVeröffentlicht - 30 Sept. 2019
Extern publiziertJa

Abstract

Let \(\ell\) be a prime number. We show that the Morita Frobenius number of an \(\ell\)-block of a quasi-simple finite group is at most 4 and that the strong Frobenius number is at most \(4|D|^2!\), where D denotes a defect group of the block. We deduce that a basic algebra of any block of the group algebra of a quasi-simple finite group over an algebraically closed field of characteristic \(\ell\) is defined over a field with \(\ell^a\) elements for some \(a \leq 4\). We derive consequences for Donovan's conjecture. In particular, we show that Donovan's conjecture holds for \(\ell\)-blocks of special linear groups.

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Rationality of blocks of quasi-simple finite groups. / Farrell, Niamh; Kessar, Radha.
in: Representation Theory, Jahrgang 23, Nr. 11, 30.09.2019, S. 325-349.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Farrell N, Kessar R. Rationality of blocks of quasi-simple finite groups. Representation Theory. 2019 Sep 30;23(11):325-349. doi: 10.1090/ert/530
Farrell, Niamh ; Kessar, Radha. / Rationality of blocks of quasi-simple finite groups. in: Representation Theory. 2019 ; Jahrgang 23, Nr. 11. S. 325-349.
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