On the stable Andreadakis problem

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.