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.
Field extension, separable extension, simple extension, radical extension, G--Cogalois extension, unique subfield property, classical Kummer extension.
ALBU, TOMA (2002) "Field Extensions Having the Unique Subfield Property, and G-Cogalois Extensions," Turkish Journal of Mathematics: Vol. 26: No. 4, Article 5. Available at: https://journals.tubitak.gov.tr/math/vol26/iss4/5