This article is cited in 7 papers

Covers in the lattice of varieties of $m$-groups

A. V. Zenkov

Altai State Agricultural University

Abstract: We consider some questions on covers in the lattice of varieties of $m$-groups. We prove the existence of a nonabelian cover of the smallest nontrivial variety of $m$-groups. We show that there exists an uncountable set of o-approximable varieties of $m$-groups each of which has continuum many o-approximable covers. In the lattice of o-approximable varieties of $m$-groups we find a variety that has no covers in this variety and no independent basis of identities.

UDC: 512.545

Received: 25.10.2004

 English version: Siberian Mathematical Journal, 2006, 47:1, 58–63

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