A generalization of Marshall’s equivalence relation

Efrat, Ido

doi:10.1090/S0002-9947-05-03776-1

A generalization of Marshall’s equivalence relation
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Trans. Amer. Math. Soc. 358 (2006), 2561-2577 Request permission

Abstract:

For $p$ prime and for a field $F$ containing a root of unity of order $p$, we generalize Marshall’s equivalence relation on orderings to arbitrary subgroups of $F^{\times }$ of index $p$. The equivalence classes then correspond to free pro-$p$ factors of the maximal pro-$p$ Galois group of $F$. We generalize to this setting results of Jacob on the maximal pro-$2$ Galois group of a Pythagorean field.

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