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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A generalization of Marshall's equivalence relation


Author: Ido Efrat
Journal: Trans. Amer. Math. Soc. 358 (2006), 2561-2577
MSC (2000): Primary 12E30; Secondary 12J15, 19C99, 12J99
Published electronically: September 22, 2005
MathSciNet review: 2204044
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03776-1
PII: S 0002-9947(05)03776-1
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.