PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 38(52), pp. 83--85 (1985)
ON A THEOREM OF SUTOV
Sava Krsti\'cMatematicki institut SANU, Beograd, Yugoslavia
Abstract: This note deals with formulas occurring in Mal'cev's and Sutov's axiomatizations of the class of semigroups embeddable in a group. Assuming $\alpha$ and $\beta$ are schemes as defined by Mal'cev and $T(\alpha)$, $T(\beta)$ corresponding Mal'cev quasi-identities and $T(\beta,x)$ the Sutov quasi-identity arising from $T(\beta)$ it is proved that there exists a semigroup on which $T(\beta,x)$ is true and $T(\alpha)$ is not whenever $\alpha$ is irreducible and $|\alpha| > |\beta|/2+2$.
Classification (MSC2000): 20M10, 08M05
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© 2001 Mathematical Institute of the Serbian Academy of Science and Arts