Rationality of blocks of quasi-simple finite groups

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

Authors

  • Niamh Farrell
  • Radha Kessar

External Research Organisations

  • University of Kaiserslautern
  • University of London
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Details

Original languageEnglish
Pages (from-to)325-349
Number of pages25
JournalRepresentation Theory
Volume23
Issue number11
Publication statusPublished - 30 Sept 2019
Externally publishedYes

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.

Keywords

    math.RT

ASJC Scopus subject areas

Cite this

Rationality of blocks of quasi-simple finite groups. / Farrell, Niamh; Kessar, Radha.
In: Representation Theory, Vol. 23, No. 11, 30.09.2019, p. 325-349.

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

Farrell N, Kessar R. Rationality of blocks of quasi-simple finite groups. Representation Theory. 2019 Sept 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 ; Vol. 23, No. 11. pp. 325-349.
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