Commutative loops of exponent 3 with x.(x.y)2=y2

• Autorzy: Armanious, M.
• Języki publikacji: EN

Abstrakty

EN

It is well known that the class of Hall triple systems [5], Steiner triple systems in which each triangle generates an affine plane over GF(3), corresponds to the class of commutative Moufang loops of exponent 3 [6]. In this paper, we extend the class of algebras to the class of all commutative loops of exponent 3 satisfying the identity x.(x.y)2=y2, corresponding to the class of all Steiner triple systems. Such a commutative loop of exponent 3 with x . (x o y)2 = y2 is polynomially equivalent to a squag.

Słowa kluczowe

EN

commutative loops; binary systems; Steiner systems; universal algebra; automorphisms

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 3
• Strony: 469-475
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Armanious, M.

• Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt

Bibliografia

• [1] R. H. Bruck, A Survey of Binary Systems, Springer, Heidelberg 1971.
• [2] B. Ganter, H. Werner, Co-ordinatizing Steiner systems, Ann. Discrete Math. 7 (1980), 3-24.
• [3] G. Grätzer, Universal Algebra, D. vein Nostrand Company, Inc. Princeton, New Jersey, Toronto, London, Melbourne 1968.
• [4] A. J. Guelzow, Representation of finite nilpotent squags, Discrete Math. 154 (1996), 63-76.
• [5] M. Hall, Jr, Automorphisms of Steiner triple systems, IBM J. 5 (1960), 460-472.
• [6] S. Klossek, Kommutative Spiegelungsraume, Mitt. Math. Sem. Univ. Giessen 117 (1975).
• [7] R. W. Quackenbush, Varieties of Steiner loops and Steiner quasigroups, Canadian. J. Math. 28 (1978), 1187-1198.