Abstract

Let \(\mathcal{M}\) be a quasivariety generated by a relatively free group in a class of nilpotent groups of step \(\leq 2\) with commutator subgroups of prime exponent \(p,\) \(p\neq 2.\) A class \(L(\mathcal{M})\) of all groups \(G\) the normal closure of any element in which belongs to \(\mathcal{M}\) is called the Levi class generated by \(\mathcal{M}.\) It is proved that \(L(\mathcal{M})\) has finite axiomatic rank, i.e., \(L(\mathcal{M})\) can be defined by a system of quasi-identities with a finite number of variables.

中文翻译：

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幂零群的几乎阿贝尔拟变异产生的Levi类的公理等级。

摘要

让\（\ mathcal {M} \）是在一类步骤的幂零群的由相对自由基产生的quasivariety \（\当量2 \）与原指数的换向器子群\（P，\） \（P \ neq 2. \）所有组的一个类\（L（\ mathcal {M}）\）\（G \）任何属于\（\ mathcal {M} \）的元素的正常闭包称为Levi \（\ mathcal {M}。\）生成的类证明\（L（\ mathcal {M}）\）具有有限的公理等级，即\（L（\ mathcal {M}）\）可以是由具有有限数量变量的准标识系统定义。