Let , or , where q is a power of some prime number p, let U denote a Sylow p-subgroup of G and let R be a commutative ring in which p is invertible. Let denote the derived subgroup of U and let . The aim of this Note is to prove that the R-algebras RG and are Morita equivalent (through the natural functor RG-mod → -mod, ).
Soit , ou , où q est une puissance dʼun nombre premier p, soit U un p-sous-groupe de Sylow de G et soit R un anneau commutatif dans lequel p est inversible. Soit le groupe dérivé de U et soit . Le but de cette Note est de montrer que les R-algèbres RG et sont Morita équivalentes (à travers le foncteur naturel RG-mod → -mod, ).
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Cédric Bonnafé 1
@article{CRMATH_2011__349_13-14_731_0, author = {C\'edric Bonnaf\'e}, title = {A progenerator for representations of $ {\mathbf{SL}}_{n}({\mathbb{F}}_{q})$ in transverse characteristic}, journal = {Comptes Rendus. Math\'ematique}, pages = {731--733}, publisher = {Elsevier}, volume = {349}, number = {13-14}, year = {2011}, doi = {10.1016/j.crma.2011.06.008}, language = {en}, }
TY - JOUR AU - Cédric Bonnafé TI - A progenerator for representations of $ {\mathbf{SL}}_{n}({\mathbb{F}}_{q})$ in transverse characteristic JO - Comptes Rendus. Mathématique PY - 2011 SP - 731 EP - 733 VL - 349 IS - 13-14 PB - Elsevier DO - 10.1016/j.crma.2011.06.008 LA - en ID - CRMATH_2011__349_13-14_731_0 ER -
Cédric Bonnafé. A progenerator for representations of $ {\mathbf{SL}}_{n}({\mathbb{F}}_{q})$ in transverse characteristic. Comptes Rendus. Mathématique, Volume 349 (2011) no. 13-14, pp. 731-733. doi : 10.1016/j.crma.2011.06.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.06.008/
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