Field extensions having the unique subfield property, and G-Cogalois extensions

Abstract

We present a short proof, based on Cogalois Theory, of a result due to Acosta de Orozco and Vélez (1982, J. Number Theory 15, 388-405) characterizing separable simple radical field extensions with the unique subfield property, and prove that these extensions are precisely the simple G--Cogalois extensions with a cyclic Kneser group.