The identities of a group with nilpotent commutator subgroup are finitely based
Izvestiya. Mathematics , Tome 37 (1991) no. 3, pp. 539-553

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It is shown that the identities of a group with nilpotent commutator subgroup are finitely based. It follows that the identities of a connected matrix group over a field are finitely based.
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     author = {A. N. Krasilnikov},
     title = {The identities of a group with nilpotent commutator subgroup are finitely based},
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A. N. Krasilnikov. The identities of a group with nilpotent commutator subgroup are finitely based. Izvestiya. Mathematics , Tome 37 (1991) no. 3, pp. 539-553. http://geodesic.mathdoc.fr/item/IM2_1991_37_3_a4/