Quaternionic Starters

Abstract

Let m be an integer, m ≥ 2 and set n = 2^m. Let G be a non-cyclic group of order 2n admitting a cyclic subgroup of order n. We prove that G always admits a starter and so there exists a one–factorization of K_{2 n} admitting G as an automorphism group acting sharply transitively on vertices. For an arbitrary even n > 2 we also show the existence of a starter in the dicyclic group of order 2n.