On the stable Andreadakis problem

[摘要] Let F-n be the free group on n generators. Consider the group I A(n) of automorphisms of F-n acting trivially on its abelianization. There are two canonical filtrations on I A(n): the first one is its lower central series Gamma(*); the second one is the Andreadakis filtration A(*), defined from the action on F-n. In this paper, we establish that the canonical morphism between the associated graded Lie rings L(Gamma(*)) and L(A(*)) 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. (C) 2019 Elsevier B.V. All rights reserved.

[发布日期] 2019-12-01

[关键词] Automorphisms of free groups;Filtrations on groups;Lie algebras;Johnson morphisms;Free differential calculus;Congruence groups