Hopf--Galois structures of cyclic type on parallel extensions of prime power degree

Andrew Darlington, Cindy Tsang

Let $L/K$ be any finite separable extension with normal closure $\tilde{L}/K$. An extension $L^{\prime }/K$ is said to be $\textit{parallel to $L/K$}$ if $L^{\prime }$ is an intermediate field o…