This article is cited in 4 papers

The axiomatic rank of a quasivariety containing a free solvable group

A. I. Budkin


Abstract: 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.

UDC: 519.48

MSC: Primary 20E10; Secondary 20E05, 20F16

Received: 23.07.1979

 English version: Mathematics of the USSR-Sbornik, 1981, 40:4, 583–590

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