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

作者：Tsang, Cindy

来源：Journal of Number Theory, 2020, 214: 286-311.

DOI：10.1016/j.jnt.2020.04.003

• Hopf-Galois structures
• Holomorph
• Regular subgroups
• Almost simple groups

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.

• 单位
  中山大学