A GALOIS EXTENSION WITH GALOIS GROUP DIHEDRAL GROUP OR GENERALIZED QUATERNION GROUP

Title & Authors
A GALOIS EXTENSION WITH GALOIS GROUP DIHEDRAL GROUP OR GENERALIZED QUATERNION GROUP
Hwang, Yoon-Sung;

Abstract
Let L/F be a Galois quadratic extension such that F contains a primitive n-th root of 1. Let N = L($\small{{\alpha}^{{\frac{1}{n}}}$) where $\small{{\alpha}{\in}L{\ast}}$. We show that if $\small{N_{L/F}({\alpha})\;{\in}L^n{\cap}F}$, and [N : L] = m, then $\small{G(N/ F) {\simeq}D_m}$ or generalized quaternion group whether $\small{N_{L/F}({\alpha})\;{\in}\;F^n\;or\;{\notin}F^n}$, respectively.
Keywords
Galois extension;Kummer extension;
Language
English
Cited by
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