Geodesic
On the problem of a finite basis of identities in groups
Izvestiya. Mathematics , Tome 4 (1970) no. 2, pp. 381-389

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This paper contains a proof that the set of varieties of groups has the cardinality of the continuum. This implies the existence of an infinite system of group identities not equivalent to any finite system. 
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     title = {On the problem of a finite basis of identities in groups},
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A. Yu. Ol'shanskii. On the problem of a finite basis of identities in groups. Izvestiya. Mathematics , Tome 4 (1970) no. 2, pp. 381-389. http://geodesic.mathdoc.fr/item/IM2_1970_4_2_a6/