Geodesic
Inherently nonfinitely based finite semigroups
Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 155-166

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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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     author = {M. V. Sapir},
     title = {Inherently nonfinitely based finite semigroups},
     journal = {Sbornik. Mathematics},
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     volume = {61},
     number = {1},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_61_1_a11/}
}
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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/