Abstract
Let k be an algebraically closed field of characteristic p. Let H be a normal subgroup of odd index, prime to p, in a finite group G. We prove that an indecomposable kH-module G-stable and selfdual can always be extended to G. If the kH-module is irreducible, only the odd index hypothesis is required.
There exists an exact sequence which is the obstruction to extending the action in such a way that the resulting kG-module is still selfdual. This enables us to make our results more precise.
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C. CIBILS. Représentations modulaires symétriques. J. of Algebra102, 537–555 (1986)
E.C. DADE. Extending irreducible modules. J. of Algebra72, 374–403 (1981)
H.G. QUEBBEMANN, W. SCHARLAU, M. SCHULTE. Quadratic and hermitian forms in additive and abelian categories. J. of Algebra59, 264–289 (1979)
J. THEVENAZ. Extensions of group representations from a normal subgroup. Comm. in Algebra11(4), 391–425 (1983)
H. ZASSENHAUS. “The theory of groups” (Chelsea, New York 1958)
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1 Au bénéfice d'une bourse du Fonds National Suisse de la Recherche Scientifique. Je remercie les membres de l'Equipe des groupes finis de Paris pour leur accueil
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Cibils, C. Etendre les representations autoduaies. Manuscripta Math 57, 477–496 (1987). https://doi.org/10.1007/BF01168673
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DOI: https://doi.org/10.1007/BF01168673