Geodesic
On a Theorem of Šutov
Publications de l'Institut Mathématique, _N_S_38 (1985) no. 52, p. 83 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

This note deals with formulas occurring in Mal'cev's and Šutov'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 Šutov 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 : 20M10 08M05 
@article{PIM_1985_N_S_38_52_a12,
     author = {Sava Krsti\'c},
     title = {On a {Theorem} of {\v{S}utov}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {83 },
     publisher = {mathdoc},
     volume = {_N_S_38},
     number = {52},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1985_N_S_38_52_a12/}
}
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Sava Krstić. On a Theorem of Šutov. Publications de l'Institut Mathématique, _N_S_38 (1985) no. 52, p. 83 . http://geodesic.mathdoc.fr/item/PIM_1985_N_S_38_52_a12/