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- W4320341851 abstract "We are interested in a class of groups, quasi-Frobenius groups (with involutions), whose internal structure generalizes that of the classical groups GA1(C), PGL 2(C) and SO3(R) : a subgroup and its conjugates, of finite index in their normalizer and trivial mutual intersection, cover generically the ambient group. From the perspective of model theory, we work with the hypothesis of the existence of a good notion of dimension on definable sets (we must distinguish between the o-minimal case and the ranked case). We pay special attention to the ranked case. By studying the geometry of incidence induced by involutions, we sketch a classification of quasi-Frobenius groups and thus determine under which conditionsclassical groups can be identified in a dimensional framework -- -- Nous nous int'eressons `a une classe de groupes, les quasi-groupes de Frobenius (avec involutions), dont la structure interne g'en'eralise celle des groupes classiques GA1(C), PGL2(C) et SO3(R) : un sous-groupe et ses conjugu'es, d'indice fini dans leur normalisateur et d'intersection mutuelle triviale, recouvrent g'en'eriquement le groupe ambiant. Dans la perspective de la th'eorie des mod`eles, nous travaillons avec l'hypoth`ese de l'existence d'une bonne notion dimension sur les ensembles d'efinissables (il faut distinguer le cas o-minimal et le cas rang'e). Nous accordons une attention particuli`ere au cas rang'e. En 'etudiant la g'eom'etrie d'incidence induite par les involutions, nous esquissons une classification des quasi-groupes de Frobenius et nous d'eterminons ainsi sous quelles conditions des groupes classiques peuvent ^etre identifi'es dans un cadre dimensionnel." @default.
- W4320341851 created "2023-02-13" @default.
- W4320341851 creator A5033754318 @default.
- W4320341851 date "2022-03-10" @default.
- W4320341851 modified "2023-09-24" @default.
- W4320341851 title "Quasi groupes de Frobenius dimensionnels" @default.
- W4320341851 hasPublicationYear "2022" @default.
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