Results related to Huppert’s - conjecture
We improve a few results related to Huppert’s - conjecture. We also generalize a result about the covering number of character degrees to arbitrary finite groups.
...-Ringstrukturen auf dem Burnsidering der Permutationsdarstellungen einer endlichen Gruppe.
Schur Indices and Modular Representations.
Semilinear Automorphisms and Dimension Functions for Certain Characters of Finite Chevalley Groups.
Some Applications of a Fundamental Theorem by Gluck and Wolf in the Character Theory of Finite Groups.
Some problems in number theory that arise from group theory.
In this expository paper, we present several open problerns in number theory that have arisen while doing research in group theory. These problems are on arithmetical functions or partitions. Solving some of these problems would allow to solve some open problem in group theory.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
Some remarks on Dade's conjecture.
Some remarks on G-functors and the Brauer morphism.
Some remarks on induced representations of infinite discrete groups.
Some results on -groups
Some simple groups which are determined by the set of their character degrees. II
Spaces of geometrically finite representations.
Special representations of some simple groups with minimal degrees.
Special representations of the Borel and maximal parabolic subgroups of .
Splitting fields and group characters.
Standard character condition for table algebras.
Subgroups of odd depth—a necessary condition
This paper gives necessary and sufficient conditions for subgroups with trivial core to be of odd depth. We show that a subgroup with trivial core is an odd depth subgroup if and only if certain induced modules from it are faithful. Algebraically this gives a combinatorial condition that has to be satisfied by the subgroups with trivial core in order to be subgroups of a given odd depth. The condition can be expressed as a certain matrix with -entries to have maximal rank. The entries of the matrix...
Supersymmetry classes of tensors
We introduce the notion of a supersymmetry class of tensors which is the ordinary symmetry class of tensors with a natural ℤ₂-gradation. We give the dimensions of even and odd parts of this gradation as well as their natural bases. Also we give a necessary and sufficient condition for the odd or even part of a supersymmetry class to be zero.
Sur les représentations de Krammer génériques
Nous définissons une représentation des groupes d’Artin de type par monodromie de systèmes KZ généralisés, dont nous montrons qu’elle est isomorphe à la représentation de Krammer généralisée définie originellement par A.M.Cohen et D.Wales, et indépendamment par F.Digne. Cela implique que tous les groupes d’Artin purs de type sphérique sont résiduellement nilpotents-sans-torsion, donc (bi-)ordonnables. En utilisant cette construction nous montrons que ces représentations irréductibles sont Zariski-denses...
Sur l'Indice de Schur Dans les Groupes Dont les Caracteres Sont a Valeurs Rationnelles