Geodesic
The axiomatic rank of a~quasivariety containing a~free solvable group
Sbornik. Mathematics, Tome 40 (1981) no. 4, pp. 583-590

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Let $\mathfrak P$ be the class of groups for which the commutator subgroup of each subgroup intersects the center of that subgroup in the identity. In this paper it is shown that if a quasivariety $\mathfrak M$ contains a non-Abelian group free in $\mathfrak A^2$ and if $\mathfrak M\subseteq\mathfrak P$, then $\mathfrak M$ cannot be given by a system of quasi-identities in a finite number of variables. Bibliography: 9 titles. 
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     author = {A. I. Budkin},
     title = {The axiomatic rank of a~quasivariety containing a~free solvable group},
     journal = {Sbornik. Mathematics},
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A. I. Budkin. The axiomatic rank of a~quasivariety containing a~free solvable group. Sbornik. Mathematics, Tome 40 (1981) no. 4, pp. 583-590. http://geodesic.mathdoc.fr/item/SM_1981_40_4_a6/