Abstract
We previously described the Galois module structures of pth-power class groups K×/K×p, where K/F is a cyclic extension of degree p over a field F containing a primitive pth root of unity. That description relied upon arithmetic invariants associated with K/F. Here we construct field extensions K/F with prescribed arithmetic invariants, thus completing the classification of Galois modules K×/K×p.
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Research supported in part by Natural Sciences and Engineering Research Council of Canada grant R0370A01, by the special Dean of Science Fund at the University of Western Ontario, and by a Distinguished Research Professorship at the University of Western Ontario for 2004/2005.
Supported by the Mathematical Sciences Research Institute, Berkeley.
Research supported in part by National Security Agency grant MDA904-02-1-0061.
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Mináč, J., Swallow, J. Galois modules appearing as pth-power classes of units of extensions of degree p. Math. Z. 250, 907–914 (2005). https://doi.org/10.1007/s00209-005-0785-x
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DOI: https://doi.org/10.1007/s00209-005-0785-x