On the Andreadakis Problem for Subgroups of $IA_n$

International audienceLet Fn be the free group on n generators. Consider the group IAn of automorphisms of Fn acting trivially on its abelianization. There are two canonical filtrations on IAn⁠: the 1st one is its lower central series Γ∗⁠; the 2nd one is the Andreadakis filtration A∗⁠, defined from the action on Fn⁠. The Andreadakis problem consists in understanding the difference between these filtrations. Here, we show that they coincide when restricted to the subgroup of triangular automorphisms and to the pure braid group