Automatic realization of Hopf Galois structures

2020/06/12 by Crespo, Teresa · 2 citations
#12F10 #16T05 #20B05 #20B35 #20D20 #20D45 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2006.07303

Abstract

We consider Hopf Galois structures on a separable field extension L/K of degree pⁿ, for p an odd prime number, n≥ 3. For p > n, we prove that L/K has at most one abelian type of Hopf Galois structures. For a nonabelian group N of order pⁿ, with commutator subgroup of order p, we prove that if L/K has a Hopf Galois structure of type N, then it has a Hopf Galois structure of type A, where A is an abelian group of order pⁿ and having the same number of elements of order p^m as N, for 1≤ m ≤ n.

Cited by

• Hopf--Galois structures of cyclic type on parallel extensions of prime power degree
• Hopf-Galois structures on separable field extensions of degree related to Cunningham chains

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