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 one-relator pro-p groups which may not be ruled out as absolute Galois groups employing the quadraticity of Galois cohomology (a consequence of Rost-Voevodsky Theorem), or the vanishing of Massey products in Galois cohomology.
Quadrelli, C. (2022). Two families of pro-p groups that are not Absolute Galois Groups. JOURNAL OF GROUP THEORY, 25(1), 25-62 [10.1515/jgth-2020-0186].
Two families of pro-p groups that are not Absolute Galois Groups
Quadrelli, C
2022
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 one-relator pro-p groups which may not be ruled out as absolute Galois groups employing the quadraticity of Galois cohomology (a consequence of Rost-Voevodsky Theorem), or the vanishing of Massey products in Galois cohomology.
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