Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T18:48:04.758Z Has data issue: false hasContentIssue false
  • English
  • Français

Varieties Of Steiner Loops and Steiner Quasigroups

Published online by Cambridge University Press:  20 November 2018

Robert W. Quackenbush
Robert W. Quackenbush*
Affiliation:
University of Manitoba, Winnipeg, Manitoba
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A Steiner Triple System (STS) is a pair (P, B) where P is a set of points and B is a set of 3-elenient subsets of P called blocks (or triples) such that for distinct p, q ∈ P there is a unique block b ∈ B with ﹛p, q) ⊂ b. There are two well-known methods for turning Steiner Triple Systems into algebras; both methods are due to R. H. Bruck [1]. Each method gives rise to a variety of algebras; in this paper we will study these varieties.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 6 , 01 December 1976 , pp. 1187 - 1198
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Bruck, R. H., A survey of binary systems (Springer-Verlag, Heidelberg, 1968).Google Scholar
2. Doyen, J., Sur la structure de certaines systèmes triples de Steiner, Math. Z. Ill (1969), 289–300.Google Scholar
3. Gratzer, G., Universal algebra (Van Nostrand, Princeton, 1968).Google Scholar
4. Metz, R. and Werner, H., On automorphism groups of finite Steiner triple systems, preprint.Google Scholar
5. Mitschke, A. and Werner, H., On groupoids representable by vector spaces over finite fields, Arch. der Math. 24 (1973), 14–20.Google Scholar
6. Quackenbush, R., Equational classes generated by finite algabras, Alg. Univ. / (1971), 265–266.Google Scholar
7. Quackenbush, R., Structure theory for equational classes generated by quasi-primal algebras, Trans. Amer. Math. Soc. 187 (1974), 127–145.Google Scholar
8. Werner, H., Congruences on products of algebras and functionally complete algebras, Alg. Univ. 4 (1974), 99–105.Google Scholar
9. Werner, H., Produkte von Kongruenzklassengeometrien universeller Algebren, Math. Z. 121 (1971), 111–140.Google Scholar