Abelian Hopf Galois structures on prime-power Galois field extensions
Abelian Hopf Galois structures on prime-power Galois field extensions
The main theorem of this paper is that if $(N, +)$ is a finite abelian $p$-group of $p$-rank $m$ where $m+1< p$, then every regular abelian subgroup of the holomorph of $N$ is isomorphic to $N$. The proof utilizes a connection, observed by Caranti, Dalla Volta, and Sala, between regular …