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September 30, 20250 citationsOpen Access

The Elementary Type Conjecture for Maximal Pro-p Galois groups

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IEIdo Efrat

Key Points

  • The study connects the elementary type conjecture to maximal pro-p Galois groups, emphasizing significant implications for Galois theory.
  • A focus on the strong arithmetical variant proves critical, revealing links to pro-p Demuskin groups in Galois groups.
  • Several variants of the conjecture aid in understanding connections to other fields and Galois theories, enhancing overall comprehension.
  • The investigation showcases potential applications of these findings in field theory and their broader implications in mathematical conjectures.

Abstract

The Elementary Type Conjecture in Galois theory provides a concrete inductive description of the finitely generated maximal pro-p Galois groups GF (p) of fields F containing a root of unity of order p. We describe several variants of this conjecture, and prove various connections between these variants and other conjectures in field and Galois theory. We focus on a strong arithmetical variant of the conjecture, and its implications to the realization of pro-p Demuskin groups as Galois groups.

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Cite This Study

Ido Efrat (2025) studied this question.

synapsesocial.com/papers/68dc1e358a7d58c25ebb1707https://doi.org/10.48550/arxiv.2509.10168
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