On ℤ_N\rtimesℤ₂-Hopf-Galois structures

2021/08/21 by Namrata Arvind, Arvind, Namrata, Saikat Panja +1
Mathematics · #12F10 #16T05 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2108.11322

openalex publication_date 2021/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K/F be a finite Galois extension of fields with Gal(K/F)=Γ. In an earlier work of Timothy Kohl, the author enumerated dihedral Hopf-Galois structures acting on dihedral extensions. Dihedral group is one particular example of semidirect product of ℤ_n and ℤ₂. In this article we count the number of Hopf-Galois structures with Galois group Γ of type G, where Γ,G are groups of the form ℤ_N\rtimes_ϕℤ₂ when N is odd with radical of N being a Burnside number. As an application we also find the corresponding number of skew braces.

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