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

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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 
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/
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     title = {On a {Theorem} of {\v{S}utov}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {83 },
     year = {1985},
     volume = {_N_S_38},
     number = {52},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1985_N_S_38_52_a12/}
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