A generalization of Marshall’s equivalence relation
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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.References
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Additional Information
- Ido Efrat
- Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, Be’er-Sheva 84105, Israel
- Email: efrat@math.bgu.ac.il
- Received by editor(s): September 27, 2003
- Received by editor(s) in revised form: June 20, 2004
- Published electronically: September 22, 2005
- Additional Notes: This research was supported by the Israel Science Foundation grant No. 8008/02–1
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 2561-2577
- MSC (2000): Primary 12E30; Secondary 12J15, 19C99, 12J99
- DOI: https://doi.org/10.1090/S0002-9947-05-03776-1
- MathSciNet review: 2204044