RESOLVABLE MENDELSOHN DESIGNS and FINITE FROBENIUS GROUPS

Abstract

We prove the existence and give constructions of a-fold perfect resolvable-Mendelsohn design for any integers k\geq 2]]> with such that there exists a finite Frobenius group whose kernel has order and whose complement contains an element of order, where is the least prime factor of. Such a design admits as a group of automorphisms and is perfect when is a prime. As an application we prove that for any integer in prime factorisation and any prime dividing for, there exists a resolvable perfect-Mendelsohn design that admits a Frobenius group as a group of automorphisms. We also prove that, if is even and divides for, then there are at least resolvable-Mendelsohn designs that admit a Frobenius ..