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 [InlineMediaObject not available: see fulltext.] 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.