LAUSR

Abstract Fix an arbitrary prime p. Let F be a field containing a primitive p-th root of unity, with absolute Galois group G F , and let H n denote its mod p cohomology group H n ( G F , Z / p Z ) . The triple Massey product (abbreviated 3MP) of weight ( n , k , m ) ∈ N 3 is a partially defined, multi-valued function 〈 ⋅ , ⋅ , ⋅ 〉 : H n × H k × H m → H n + k + m − 1 . In this work we prove that for an odd prime p, any defined 3MP of weight ( 1 , k , 1 ) contains zero.