Geodesic
Inherently nonfinitely based finite semigroups
Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 155-166 
M. V. Sapir. Inherently nonfinitely based finite semigroups. Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 155-166. http://geodesic.mathdoc.fr/item/SM_1988_61_1_a11/
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     author = {M. V. Sapir},
     title = {Inherently nonfinitely based finite semigroups},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_61_1_a11/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A locally finite variety is called inherently nonfinitely based if it is not contained in any finitely based locally finite variety. A finite universal algebra is called inherently nonfinitely based if it generates an inherently nonfinitely based variety. In this paper a description of inherently nonfinitely based finite semigroups is given; it is proved that the set of such semigroups is recursive and that the property of a finite semigroup to be inherently nonfinitely based is mainly determined by the structure of its subgroups. It is also shown that there exists a unique minimal inherently nonfinitely based variety of semigroups consisting not only of groups. It is not known whether there exists an inherently nonfinitely based variety of groups. Bibliography: 18 titles.

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