S. V. Varaksin, A. V. Zenkov, “On representations of <nobr>$m$</nobr>-groups”, Sibirsk. Mat. Zh., 2013, Volume 54, Number 2,Pages <nobr>298

This article is cited in 5 papers

On representations of $m$-groups

S. V. Varaksin^a, A. V. Zenkov^b

^a Altai State University, Barnaul, Russia
^b Altai State University of Agriculture, Barnaul, Russia

Abstract: We obtain a description of the $m$-transitive representations of an arbitrary $m$-group. Some necessary and sufficient conditions are given for an $m$-group to admit a faithful $m$-transitive representation. We establish as a corollary that each subdirectly $m$-indecomposable group admits a faithful $m$-transitive representation, and so each variety of $m$-groups is generated by its $m$-transitive groups.

Keywords: $m$-group, $m$-transitive representation, subdirectly indecomposable $m$-group.

UDC: 512.545

Received: 03.05.2011