The Hopf Galois Property in Subfield Lattices - Crespo, Teresa; Rio, Anna; Vela, Montserrat (Communications in algebra, 2016)
Let K/k be a finite separable extension, n its degree and its Galois closure. For n ≤ 5, Greither and Pareigis show that all Hopf Galois extensions are either Galois or almost classically Galois and they determine the Hopf Galois character of K/k according to the Galois group (or the degree) of . In this paper we study the case n = 6, and intermediate extensions F/k such that , for degrees n = 4, 5, 6. We present an example of a non almost classically Galois Hopf Galois extension of ℚ of the smallest possible degree and new examples of Hopf Galois extensions. In the last section we prove a transitivity property of the Hopf Galois condition.