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

Letpbe a prime number,Ka field with characteristic notpand containing thepth roots of unity, andE/Kan abelian exponentpGalois extension. We prove explicit formulas for the construction of fieldsN/Kwith Galois group a centralp-extension of Gal(E/K). These formulas do not require the solution of a linear system of equations in the field extension, as do the formulas of Massy [J. Algebra109(1987), 508–535]. In our study we develop generalizations of theorems of Serre and Fröhlich on representing obstructions to embedding problems and theorems of Crespo on explicitly constructing solution fields.