This article is cited in 3 papers

Two questions in the theory of $m$-groups

A. V. Zenkov^a, O. V. Isaeva<sup>b

a</sup> Altai State University of Agriculture, Barnaul, Russia
^b Altai State University, Barnaul, Russia

Abstract: We study the structure of primitive $m$-groups in the variety of normal-valued $m$-groups. We prove that $\mathscr{U(V}_1\lor \mathscr V_2)=\mathscr{UV}_1\lor\mathscr{UV}_2$ for arbitrary varieties of $m$-groups $\mathscr U$, $\mathscr V_1$ and $\mathscr V_2$.

Keywords: $m$-transitive representation, primitive representation, normal-valued $m$-group, subdirectly indecomposable $m$-group, variety of $m$-groups.

UDC: 512.545

Received: 10.03.2014

 English version: Siberian Mathematical Journal, 2014, 55:6, 1042–1044

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