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On tamely ramified pro-p-extensions over ${\mathbb Z}_p$-extensions of ${\mathbb Q}$

Published online by Cambridge University Press:  20 November 2013

TSUYOSHI ITOH  and
YASUSHI MIZUSAWA
TSUYOSHI ITOH
Affiliation:
Division of Mathematics, Education Center, Faculty of Social Systems Science, Chiba Institute of Technology, 2-1-1 Shibazono, Narashino, Chiba 275-0023, Japan. e-mail: tsuyoshi.itoh@it-chiba.ac.jp
YASUSHI MIZUSAWA
Affiliation:
Department of Mathematics, Nagoya Institute of Technology, Gokiso, Showa, Nagoya 466-8555, Japan. e-mail: mizusawa.yasushi@nitech.ac.jp
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Abstract

For an odd prime number p and a finite set S of prime numbers congruent to 1 modulo p, we consider the Galois group of the maximal pro-p-extension unramified outside S over the ${\mathbb Z}_p$-extension of the rational number field. In this paper, we classify all S such that the Galois group is a metacyclic pro-p group.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 156 , Issue 2 , March 2014 , pp. 281 - 294
Copyright
Copyright © Cambridge Philosophical Society 2013 

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