The strong Massey vanishing conjecture for fields with virtual cohomological dimension at most 1

Abstract We show that a strong vanishing conjecture for n -fold Massey products holds for fields of virtual cohomological dimension at most 1 using a theorem of Haran. We also prove the same for PpC fields, using results of Haran–Jarden. Finally we give a purely group-theoretical construction of a pro-2 group which satisfies the weak Massey vanishing property for every n ≥ 3, but does not satisfy the strong Massey vanishing property for n = 4.