*(N1) (A.Miasnikov) Let G be a free nilpotent group of finite rank. Suppose an element g \in G is fixed by every automorphism of G. Is it true that g = 1 ?  Background

(N2) Let G be a finitely generated nilpotent group. Is the Dehn function of G equivalent to a polynomial? Background

(N3) (B.I.Plotkin) Is it true that every locally nilpotent group is a homomorphic image of a torsion-free locally nilpotent group?

(N4) (G.Baumslag) Let G be a finitely generated torsion-free nilpotent group. Is it true that there are only finitely many non-isomorphic groups in the sequence Aut(G), Aut(Aut(G)), ... ? Background

(N5) (G.Baumslag) Is the property of being directly indecomposable decidable for finitely generated nilpotent groups?

(N6) (A.Miasnikov) Describe all finitely generated nilpotent groups of class 2 which have genus 1. (We say that a group G has genus 1, if every group with the same set of finite homomorphic images as G, is isomorphic to G).

(N7) Is every group with an Engel identity [x,y,...,y] = 1, locally nilpotent?