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cyclic extension

Proceedings of the London Mathematical Society (1)

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GALOIS MODULE STRUCTURE OF pTH-POWER CLASSES OF CYCLIC EXTENSIONS OF DEGREE pn
JÁN MINÁČ, ANDREW SCHULTZ, JOHN SWALLOW
Journal:

Proceedings of the London Mathematical Society / Volume 92 / Issue 2 / March 2006

Published online by Cambridge University Press:

20 February 2006, pp. 307-341

Print publication:

March 2006
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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\$.