Regular groups, radical rings, and Abelian Hopf Galois structures on prime-power Galois field extensions

Abstract

This is a report on joint work of the author with S. C. Featherstonhaugh and L. N. Childs, and expands slightly on the presentation given by the author at Porto Cesareo, on June 9, 2011, at the Conference on Advances in Group Theory and Applications. The full results appear in [5].