Geodesic
A basis of identities of a variety generated by a finitely-based quasi-variety of groups
Sbornik. Mathematics, Tome 189 (1998) no. 8, pp. 1115-1124 
M. I. Anokhin. A basis of identities of a variety generated by a finitely-based quasi-variety of groups. Sbornik. Mathematics, Tome 189 (1998) no. 8, pp. 1115-1124. http://geodesic.mathdoc.fr/item/SM_1998_189_8_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Examples are constructed of soluble finitely-based quasi-varieties of groups that generate non-finitely based varieties (with degree of solubility at most 7).

[1] Mazurov V. D., Khukhro E. I., Nereshennye voprosy teorii grupp. Kourovskaya tetrad, Izd-vo NII matematiko-informatsionnykh osnov obucheniya NGU, Novosibirsk, 1995

[2] Kleiman Yu. G., “O nekotorykh voprosakh teorii mnogoobrazii grupp”, Izv. AN SSSR. Ser. matem., 47:1 (1983), 37–74 | MR | Zbl

[3] Vaughan-Lee M. R., “Uncountably many varieties of groups”, Bull. London Math. Soc. Pt. 3, 2:6 (1970), 280–286 | DOI | MR | Zbl

[4] Kleiman Yu. G., “O tozhdestvakh v gruppakh”, Tr. MMO, 44, URSS, M., 1982, 62–108 | MR | Zbl

[5] Neiman Kh., Mnogoobraziya grupp, Mir, M., 1969 | MR

[6] Maltsev A. I., Algebraicheskie sistemy, Nauka, M., 1970 | MR | Zbl