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GALOIS MODULE STRUCTURE OF pTH-POWER CLASSES OF CYCLIC EXTENSIONS OF DEGREE pn

Published online by Cambridge University Press:  20 February 2006

JÁN MINÁČ ,
ANDREW SCHULTZ  and
JOHN SWALLOW
JÁN MINÁČ
Affiliation:
Department of Mathematics, Middlesex College, University of Western Ontario, London, Ontario N6A 5B7, Canadaminac@uwo.ca
ANDREW SCHULTZ
Affiliation:
Department of Mathematics, Building 380, Stanford University, Stanford, CA 94305-2125, USAaschultz@stanford.edu
JOHN SWALLOW
Affiliation:
Department of Mathematics, Davidson College, Box 7046, Davidson, NC 28035-7046, USAjoswallow@davidson.edu
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Abstract

In the mid-1960s Borevi$\setminus$v\{c\} and Faddeev initiated the study of the Galois module structure of groups of \$p\$th-power classes of cyclic extensions \$K/F\$ of \$p\$th-power degree. They determined the structure of these modules in the case when \$F\$ is a local field. In this paper we determine these Galois modules for all base fields \$F\$.

Keywords

Galois module\$p\$th-power classesnormcyclic extensionHilbert 9012F10 (primary)16D70 (secondary)
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 92 , Issue 2 , March 2006 , pp. 307 - 341
Copyright
2006 London Mathematical Society

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