The symbol length for elementary type pro-p groups and Massey products

Ido Efrat

doi:10.1016/j.jalgebra.2024.04.025

The symbol length for elementary type pro-p groups and Massey products

Ido Efrat

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For a prime number p and an integer m≥2, we prove that the symbol length of all elements of m-fold Massey products in H²(G,F_p), for pro-p groups G of elementary type, is bounded by (m²/4)+m. Assuming the Elementary Type Conjecture, this applies to all finitely generated maximal pro-p Galois groups G=G_F(p) of fields F which contain a root of unity of order p. More generally, we provide such a uniform bound for the symbol length of all pullbacks ρ^⁎(ω¯) of a given cohomology element ω¯∈Hⁿ(G¯,F_p), where G¯ is a finite p-group, n≥2, and ρ:G→G¯ is a pro-p group homomorphism.

Original language	English
Pages (from-to)	298-324
Number of pages	27
Journal	Journal of Algebra
Volume	653
DOIs	https://doi.org/10.1016/j.jalgebra.2024.04.025
State	Published - 1 Sep 2024

Keywords

Galois cohomology
Massey products
Symbol length
The Elementary Type Conjecture

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2024.04.025

Cite this

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title = "The symbol length for elementary type pro-p groups and Massey products",

abstract = "For a prime number p and an integer m≥2, we prove that the symbol length of all elements of m-fold Massey products in H2(G,Fp), for pro-p groups G of elementary type, is bounded by (m2/4)+m. Assuming the Elementary Type Conjecture, this applies to all finitely generated maximal pro-p Galois groups G=GF(p) of fields F which contain a root of unity of order p. More generally, we provide such a uniform bound for the symbol length of all pullbacks ρ⁎(ω¯) of a given cohomology element ω¯∈Hn(G¯,Fp), where G¯ is a finite p-group, n≥2, and ρ:G→G¯ is a pro-p group homomorphism.",

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author = "Ido Efrat",

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N2 - For a prime number p and an integer m≥2, we prove that the symbol length of all elements of m-fold Massey products in H2(G,Fp), for pro-p groups G of elementary type, is bounded by (m2/4)+m. Assuming the Elementary Type Conjecture, this applies to all finitely generated maximal pro-p Galois groups G=GF(p) of fields F which contain a root of unity of order p. More generally, we provide such a uniform bound for the symbol length of all pullbacks ρ⁎(ω¯) of a given cohomology element ω¯∈Hn(G¯,Fp), where G¯ is a finite p-group, n≥2, and ρ:G→G¯ is a pro-p group homomorphism.

AB - For a prime number p and an integer m≥2, we prove that the symbol length of all elements of m-fold Massey products in H2(G,Fp), for pro-p groups G of elementary type, is bounded by (m2/4)+m. Assuming the Elementary Type Conjecture, this applies to all finitely generated maximal pro-p Galois groups G=GF(p) of fields F which contain a root of unity of order p. More generally, we provide such a uniform bound for the symbol length of all pullbacks ρ⁎(ω¯) of a given cohomology element ω¯∈Hn(G¯,Fp), where G¯ is a finite p-group, n≥2, and ρ:G→G¯ is a pro-p group homomorphism.

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KW - Massey products

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KW - The Elementary Type Conjecture

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

The symbol length for elementary type pro-p groups and Massey products

Abstract

Keywords

ASJC Scopus subject areas

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