Quaternionic Starters

@article{Bonisoli2005QuaternionicS,
  title={Quaternionic Starters},
  author={Arrigo Bonisoli and Gloria Rinaldi},
  journal={Graphs and Combinatorics},
  year={2005},
  volume={21},
  pages={187-195}
}
Let m be an integer, m 2 and set n 1⁄4 2m. 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 F of K2n 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.