Geodesic
On a~basis of the product of varieties of groups.~II
Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 481-489.

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It is proved that for any finitely based variety of groups there exists a finitely based left factor such that their product is infinitely based (the left factor is a Burnside variety). 
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Yu. G. Kleiman. On a~basis of the product of varieties of groups.~II. Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 481-489. http://geodesic.mathdoc.fr/item/IM2_1974_8_3_a2/

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[4] Newman M. F., “Just non-finitely-based varieties of groups”, Bull. Austral. Math. Soc., 4 (1971), 343–348 | DOI | MR | Zbl

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