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On nondistributive Steiner quasigroups

A. Marczak — 1997

Colloquium Mathematicae

A well known result of R. Dedekind states that a lattice is nonmodular if and only if it has a sublattice isomorphic to N 5 . Similarly a lattice is nondistributive if and only if it has a sublattice isomorphic to N 5 or M 3 (see [11]). Recently a few results in this spirit were obtained involving the number of polynomials of an algebra (see e.g. [1], [3], [5], [6]). In this paper we prove that a nondistributive Steiner quasigroup (G,·) has at least 21 essentially ternary polynomials (which improves the...

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