Abstract : Let be the free group on n generators. Consider the group of automorphisms of acting trivially on its abelianization. There are two canonical filtrations on : the first one is its lower central series ⁎; the second one is the Andreadakis filtration ⁎, defined from the action on . In this paper, we establish that the canonical morphism between the associated graded Lie rings ⁎ and ⁎ is stably surjective. We then investigate a p-restricted version of the Andreadakis problem. A calculation of the Lie algebra of the classical congruence group is also included.
https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02468983 Contributeur : Accord Elsevier CCSDConnectez-vous pour contacter le contributeur Soumis le : lundi 25 octobre 2021 - 13:19:38 Dernière modification le : mercredi 23 mars 2022 - 15:50:08 Archivage à long terme le : : mercredi 26 janvier 2022 - 20:06:31
Jacques Darné. On the stable Andreadakis problem. Journal of Pure and Applied Algebra, Elsevier, 2019, 223 (12), pp.5484-5525. ⟨10.1016/j.jpaa.2019.04.010⟩. ⟨hal-02468983⟩