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Centralp-Extensions of (p, p,…,p)-Type Galois Groups

✍ Scribed by John R. Swallow

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
254 KB
Volume
186
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let p be a prime number, K a field with characteristic not p and containing the pth roots of unity, and ErK an abelian exponent p Galois extension. We prove explicit formulas for the construction of fields NrK with Galois group a central Ž . p-extension of Gal ErK . These formulas do not require the solution of a linear w system of equations in the field extension, as do the formulas of Massy J. Algebra Ž .

x 109 1987 , 508᎐535 . In our study we develop generalizations of theorems of Serre and Frohlich on representing obstructions to embedding problems and theorems of Crespo on explicitly constructing solution fields.

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