## 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/pZ). The triple Massey product 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 arbitrary prime p, any defined 3MP of weight (n,1,m), where the first and third entries are symbols, contains zero; and that any defined 3MP of weight (1,k,1), where the middle entry is a symbol, contains zero.

Original language | English |
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Pages (from-to) | 136-146 |

Number of pages | 11 |

Journal | Journal of Algebra |

Volume | 527 |

DOIs | |

State | Published - 1 Jun 2019 |

### Bibliographical note

Publisher Copyright:© 2019 Elsevier Inc.

## Keywords

- External cohomological operations
- Galois cohomology
- Massey products
- Symbols