This article is cited in 10 papers

The Levi classes generated by nilpotent groups

V. V. Lodeyshchikova

Altai State University, Barnaul

Abstract: Given an arbitrary class $M$ of groups, denote by $L(M)$ the class of all groups $G$ in which the normal closure of every element belongs to $M$. Consider the quasivariety $qF_p$ generated by the relatively free group in the class of nilpotent groups of length at most 2 with the commutant of exponent $p$ (where $p$ is an odd prime). We describe the Levi class that is generated by $qF_p$.

Keywords: quasivariety, Levi class, nilpotent group.

UDC: 512.54.01

Received: 03.06.2009

 English version: Siberian Mathematical Journal, 2010, 51:6, 1075–1080

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