Geodesic
On the problem of a finite basis of identities in groups
Izvestiya. Mathematics, Tome 4 (1970) no. 2, pp. 381-389 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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