Bulletin of the Australian Mathematical Society

Table of Contents - Volume 44 - Issue03

Research Article

Non-isomorphic 2-perfect 6-cycle systems of order 13

Rebecca A.H. Gowera1

a1 Department of Mathematics, The University of Queensland, Queensland 4072

Abstract

Running a computer search for new, cyclic, 2-perfect 6-cycle systems of order 13 and constructing the quasigroups which arise from such systems enabled the author to establish that there are at most two such non-isomorphic systems. Then by using two-variable laws of the quasigroups it is shown that there are exactly two non-isomorphic 2-perfect 6-cycle systems of order 13 which are cyclic.

(Received November 21 1990)

References

  • [1] Gower, R.A.H., Oates-Williams, S., Donovan, D. and Billington, E.J., ‘On the quasigroup variety arising from a 2-perfect 6-cycle system of order 13’, J. Combin. Math. Combin. Comput. (to appear).
  • [2] Lindner, C.C., Phelps, K.T. and Rodger, C.A., ‘The Spectrum for 2-perfect 6-cycle systems’, J. Combin. Theory A (to appear).
  • [3] Lindner, C.C., ‘Graph decompositions and quasigroup identities’, in Proceedings of the Second International Catania Combinatorial Conference, “Graphs, designs and combinatorial geometries” (Universita di Catania, Catania, Sicily, 1989 to appear).