(E1) Describe the groups over which any equation is solvable.

(E2) (M.Kervaire, F.Laudenbach) Let F_n/R = <x_1,...,x_n | r_1,...,r_m> be a presentation of a non-trivial group. Is it true that a group <x_1,...,x_n, x_{n+1} | r_1,...,r_m, s> is also non-trivial for any element s from F_{n+1} ? Background

*(E3) (L.Comerford) If an equation over a free group F has no solutions in F, is there a finite quotient of F in which the equation has no solutions? (If so, this provides another proof of Makanin's theorem). Background

(E4) (J.Birman) Let F = F_n be the free group of rank n generated by a_1,...,a_n. Is there a solution of the equation y_1 a_1 y_1^{-1} ... y_n a_n y_n^{-1} = a_1...a_n with all y_i from the second commutator subgroup F'' ? (The answer is "no" if and only if the Gassner representation of the pure braid group P_n is faithful -- cf. problem (B2)).

(E5) (G.Baumslag, A.Miasnikov, V.Remeslennikov) Is a free product of two equationally noetherian groups equationally noetherian? (A group is called equationally noetherian if every system of equations in this group is equivalent to a finite subsystem). Background

(E6) (G.Baumslag, A.Miasnikov, V.Remeslennikov) Is a free pro-p group
equationally noetherian?