5. 22/12/2025 Cindy Tsang (Ochanomizu University in Tokyo, Japan) скачать в хорошем качестве

5. 22/12/2025 Cindy Tsang (Ochanomizu University in Tokyo, Japan)

TITLE: Hopf--Galois structures of cyclic type on parallel extensions of prime power degree ABSTRACT: Let L/K be a finite separable extension with Galois closure \widetilde{L}/K. We say that L'/K is parallel to L/K if L' is an immediate field of \widetilde{L}/K and [\widetilde{L}:K]=[L:K]. Note that this notion is not symmetric. We are interested in comparing the Hopf-Galois structures on L'/K with those on L/K. In this talk, I will first explain how this problem reduces to a completely group-theoretic problem that involves the study of transitive subgroups of the holomorph. After that, I will report on some new results when the type of the Hopf-Galois structures is cyclic, and the degree of the extension is a prime power. This is joint work with Andrew Darlington.