Nonabelian Case of Hopf Galois Structures on Nonnormal Extensions of Degree pqw

Authors

  • Baraa M Jamal University of Mosul/ College of Education for Pure Sciences/ Department of Mathematics
  • Ali Alabdali University of Mosul\ College of Education for Pure Science\ Department of Mathematics

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i2.4755

Keywords:

Hopf Galois structures, field extensions, groups of square free order, Sophie Germain primes

Abstract

We look at Hopf Galois structures with square free pqw degree on separable field extensions (nonnormal) L/K. Where E/K is the normal closure of L/K, the group permutation of degree pqw is G = Gal(E/K). We study details of the nonabelian case, where Jl = ⟨σ, [τ, αl ]⟩ is a nonabelian regular subgroup of Hol(N) for 1 ≤ l ≤ w − 1. We first find the group permutation G, and then the Hopf Galois structures for each G. In this case, there exists four G such that the Hopf Galois structures are admissible within the field extensions L/K.

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Published

2023-04-30

Issue

Section

Nonlinear Analysis

How to Cite

Nonabelian Case of Hopf Galois Structures on Nonnormal Extensions of Degree pqw. (2023). European Journal of Pure and Applied Mathematics, 16(2), 1118-1127. https://doi.org/10.29020/nybg.ejpam.v16i2.4755

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