Journal article
Autoequivalences of blocks and a conjecture of Zassenhaus
Journal of pure and applied algebra, Vol.103(1), pp.23-43
1995
DOI: 10.1016/0022-4049(94)00091-V
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.
Details
- Title: Subtitle
- Autoequivalences of blocks and a conjecture of Zassenhaus
- Creators
- Frauke M BleherGerhard HissWolfgang Kimmerle
- Resource Type
- Journal article
- Publication Details
- Journal of pure and applied algebra, Vol.103(1), pp.23-43
- DOI
- 10.1016/0022-4049(94)00091-V
- ISSN
- 0022-4049
- eISSN
- 1873-1376
- Language
- English
- Date published
- 1995
- Academic Unit
- Mathematics
- Record Identifier
- 9983985999102771
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