Autoequivalences of blocks and a conjecture of Zassenhaus

• Verfasst von: Bleher, Frauke M. [VerfasserIn]
• Verfasst von: Hiss, Gerhard [VerfasserIn]
• Verfasst von: Kimmerle, Wolfgang [VerfasserIn]
• Titel: Autoequivalences of blocks and a conjecture of Zassenhaus
• Verf.angabe: Frauke M. Bleher, Gerhard Hiss, Wolfgang Kimmerle
• Jahr: 1995
• Umfang: 21 S.
• Fussnoten: Gesehen am 22.05.2023 ; Elektronische Reproduktion der Druck-Ausgabe 22. Dezember 1999
• Titel Quelle: Enthalten in: Journal of pure and applied algebra
• Ort Quelle: Amsterdam [u.a.] : North-Holland, Elsevier Science, 1971
• Jahr Quelle: 1995
• Band/Heft Quelle: 103(1995), 1, Seite 23-43
• ISSN Quelle: 1873-1376
• DOI: doi:10.1016/0022-4049(94)00091-V
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1845903579

Abstract

In this paper, we show that for every finite group with cyclic Sylow p-subgroups the principal p-block B is rigid with respect to the trivial simple module. This means that each autoequivalence which fixes the trivial simple module fixes the isomorphism class of each finitely generated B-module. As a consequence each augmentation preserving automorphism of the integral group ring of PSL(2, p), p a rational prime, is given by a group automorphism followed by a conjugation in QPSL(2, p). In particular this proves a conjecture of Zassenhaus for these groups. Finally we show the same statement for a couple of other simple groups by different methods.