Outputs (2)

On ρ-conjugate Hopf–Galois structures (2023)
Journal Article
Truman. (2023). On ρ-conjugate Hopf–Galois structures. Proceedings of the Edinburgh Mathematical Society, 66(1), 288-304. https://doi.org/10.1017/S0013091523000184

The Hopf-Galois structures admitted by a Galois extension of fields $ L/K $ with Galois group $ G $ correspond bijectively with certain subgroups of $ \mathrm{Perm}(G) $. We use a natural partition of the set of such subgroups to obtain a method for... Read More about On ρ-conjugate Hopf–Galois structures.

Hopf-Galois module structure of tamely ramified radical extensions of prime degree (2019)
Journal Article
Truman, P. J. (2020). Hopf-Galois module structure of tamely ramified radical extensions of prime degree. Journal of Pure and Applied Algebra, 224(5), Article 106231. https://doi.org/10.1016/j.jpaa.2019.106231

Let K be a number field and let L/K be a tamely ramified radical extension of prime degree p. If K contains a primitive p th root of unity then L/K is a cyclic Kummer extension; in this case the group algebra K[G] (with G = Gal(L/K)) gives the unique... Read More about Hopf-Galois module structure of tamely ramified radical extensions of prime degree.