Geodesic
Bases of the identities of products of certain varieties of groups
Matematičeskie zametki, Tome 5 (1969) no. 1, pp. 137-144.

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The following theorem is proved: The product of any variety of two-step solvable groups and a variety having a finite basis of identity relations has a finite basis of identity relations. 
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     title = {Bases of the identities of products of certain varieties of groups},
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I. D. Ivanyuta. Bases of the identities of products of certain varieties of groups. Matematičeskie zametki, Tome 5 (1969) no. 1, pp. 137-144. http://geodesic.mathdoc.fr/item/MZM_1969_5_1_a16/