A class $C$ of $m$-cycle systems is said to be equationally defined provided there exists a variety of algebraic quasigroups $V$ such that a finite quasigroup belongs to $V$ if and only if the multiplicative part of the quasigroup can be constructed from a $m$-cycle system belonging to $C$ using a given construction (too complicate to go into here). In [3] it is shown that the class of $2$-perfect $m$-cycle systems can be equationally defined for $m=3,5,$ and$7$ only. In [5] it is shown that the class of $2,3$-perfect $7$-cycle systems can be equationally defined. In this paper we extend this result by showing that the class of $2,3$-perfect $m$-cycle systems can be equationally defined for $m=8,9,$ and $11$. In each case we give a defining set of identities for the variety.

On equationally definable m-cycle systems

Rania F
2002-01-01

Abstract

A class $C$ of $m$-cycle systems is said to be equationally defined provided there exists a variety of algebraic quasigroups $V$ such that a finite quasigroup belongs to $V$ if and only if the multiplicative part of the quasigroup can be constructed from a $m$-cycle system belonging to $C$ using a given construction (too complicate to go into here). In [3] it is shown that the class of $2$-perfect $m$-cycle systems can be equationally defined for $m=3,5,$ and$7$ only. In [5] it is shown that the class of $2,3$-perfect $7$-cycle systems can be equationally defined. In this paper we extend this result by showing that the class of $2,3$-perfect $m$-cycle systems can be equationally defined for $m=8,9,$ and $11$. In each case we give a defining set of identities for the variety.
2002
$m$-cycle system, $k$-perfect $m$-cycle systems, variety of quasy groups, defining set of identities for a variety
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12317/11064
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