Commutative Quartic P-Galois Extensions Over a Field of Characteristic Not 2

Authors: ATSUSHI NAKAJIMA

Abstract: In [2], K. Kishimoto introduced the notion of P-Galois extensions and gave some fundamental properties of these extensions. P-Galois extensions relate Hopf Galois extensions, and the author treated these topics in [5]. Moreover, the cubic P-Galois extensions over a field were completely determined in [6]. Continuing [5] and [6], we classify commutative quartic P-Galois extensions over a field of characteristic not 2.

Keywords: Galois extension, P-Galois extension, quartic extension

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