Finite permutation groups with a regular dihedral subgroup, and edge-transitive dihedrants

Abstract We study finite permutation groups that contain a regular dihedral subgroup, called d-groups . In particular, a classification is given of bi-quasiprimitive d-groups. It is then applied to classify edge-transitive dihedrants of order 2 p m and valency coprime to p , where p is an odd prime and m is a positive integer.