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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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/

[1] Neumann B. H., “Identical relations in groups. I”, Math. Ann., 114 (1937), 506–525 | DOI | MR | Zbl

[2] Neimaya Kh., Mnogoobraziya grupp, Mir, M., 1969 | MR

[3] Lyndon R. C., “Two notes on nilpotent groups”, Proc. Amer. Math. Soc., 3 (1952), 579–583 | DOI | MR | Zbl

[4] Oates Sheila, Powell M. B., “Identical relations in finite groups”, J. Algebra, 1 (1964), 11–39 | DOI | MR | Zbl

[5] Cohen D. E., “On the laws of metabelian variety”, J. Algebra, 5 (1967), 267–273 | DOI | MR | Zbl