It is shown that for every admissible order v for which a cyclic Steiner triple system exists, there exists a biembedding of a cyclic Steiner quasigroup of order v with a copy of itself. Furthermore, it is shown that for each n≥2 the projective Steiner quasigroup of order 2n−1 has a biembedding with a copy of itself.
Bibliographical notePublisher: Wiley
Donovan, DM., Grannell, MJ., Griggs, TS., Lefevre, JG., & McCourt, TA. (2011). Self-embeddings of cyclic and projective Steiner quasigroups. Journal of Combinatorial Designs, 19, issue 1, 16 - 27. https://doi.org/10.1002/jcd.20258