This article is cited in 3 papers

Wreath products of the groups of monotone permutations

A. V. Zenkov

Altai State Agricultural University, Barnaul

Abstract: We introduce the concept of wreath product of the $m$-groups of permutations and prove that an $m$-transitive group of permutations with an m-congruence is embeddable into the wreath product of the suitable $m$-transitive $m$-groups of permutations. This implies that an arbitrary $m$-transitive group in the product of two varieties of $m$-groups embeds into the wreath product of the suitable $m$-transitive groups of these varieties.

Keywords: m-group, representation, $m$-congruence, wreath product.

UDC: 512.545

Received: 13.05.2010

 English version: Siberian Mathematical Journal, 2011, 52:6, 1003–1008

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