Hopf-Galois structures on finite extensions with almost simple Galois group

JOURNAL OF NUMBER THEORY

卷:214

Article

Tsang, Cindy (Sin Yi)¹ 

[1] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai, Guangdong, Peoples R China

关键词: Hopf-Galois structures;    Holomorph;    Regular subgroups;    Almost simple groups;   

DOI  :  10.1016/j.jnt.2020.04.003

来源: Elsevier

【 摘 要 】

In this paper, we study the Hopf-Galois structures on a finite Galois extension whose Galois group G is an almost simple group in which the socle A has prime index p. Each Hopf-Galois structure is associated to a group N of the same order as G. We shall give necessary criteria on these N in terms of their group-theoretic properties, and determine the number of Hopf-Galois structures associated to A x C-p , where C-p is the cyclic group of order p. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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