Affiliation:
1. Department of Mathematics and Applications , University of Milano Bicocca , 20125 Milan , Italy
Abstract
Abstract
Let 𝑝 be a prime.
We produce two new families of pro-𝑝 groups which are not realizable as absolute Galois groups of fields.
To prove this, we use the 1-smoothness property of absolute Galois pro-𝑝 groups.
Moreover, we show in these families, one has several pro-𝑝 groups which may not be ruled out as absolute Galois groups employing the quadraticity of Galois cohomology (a consequence of the norm residue theorem), or the vanishing of Massey products in Galois cohomology.
Subject
Algebra and Number Theory
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