The Hopf Galois Property in Subfield Lattices

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...

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Bibliographic Details
Published in:	Communications in algebra Vol. 44; no. 1; pp. 336 - 353
Main Authors:	Crespo, Teresa, Rio, Anna, Vela, Montserrat
Format:	Journal Article Publication
Language:	English
Published:	Taylor & Francis Group 02.01.2016
Subjects:	12 Field theory and polynomials 12F Field extensions Classificació AMS Galois theory Galois, Teoria de Holomorph Hopf algebra Hopf Galois extension Matemàtiques i estadística SEPARABLE FIELD-EXTENSIONS Teoria de nombres Àlgebra Àrees temàtiques de la UPC
ISSN:	0092-7872, 1532-4125
Online Access:	Get full text
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Summary:	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.
ISSN:	0092-7872 1532-4125
DOI:	10.1080/00927872.2014.982809