Construction of quasigroups using the singular direct product
HTML articles powered by AMS MathViewer
- by Charles C. Lindner PDF
- Proc. Amer. Math. Soc. 29 (1971), 263-266 Request permission
Abstract:
The idea of a discrete $w(x,y) = v(x,y)$ quasigroup is given along with a generalization of A. Sade’s singular direct product. These notions are then used to construct certain types of quasigroups. In particular an algebraic generalization of E. H. Moore’s construction of Steiner triple systems is obtained.References
- Jean Doyen, Sur la croissance du nombre de systèmes triples de Steiner non isomorphes, J. Combinatorial Theory 8 (1970), 424–441 (French). MR 256900
- Charles C. Lindner, The generalized singular direct product for quasigroups, Canad. Math. Bull. 14 (1971), 61–63. MR 291341, DOI 10.4153/CMB-1971-011-0
- C. C. Lindner, Identities preserved by the singular direct product, Algebra Universalis 1 (1971), no. 1, 86–89. MR 288203, DOI 10.1007/BF02944960
- E. Hastings Moore, Concerning triple systems, Math. Ann. 43 (1893), no. 2-3, 271–285. MR 1510812, DOI 10.1007/BF01443649
- A. Sade, Produit direct-singulier de quasigroupes orthogonaux et anti-abéliens, Ann. Soc. Sci. Bruxelles Sér. I 74 (1960), 91–99 (French). MR 140599
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 263-266
- MSC: Primary 20.95; Secondary 05.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0280635-1
- MathSciNet review: 0280635