MATHEMATICS

Presentations and Cartesian product of $m$-groups

A. V. Zenkov

Altai State Agricultural University, Barnaul, Russian Federation

Abstract: It is shown that any convex $m$-subgroup of a Cartesian product of $m$-groups that admits a faithful $m$-transitive representation is a convex m-subgroup of an appropriate projection of the Cartesian product of $m$-groups. This implies that the Cartesian product of $m$-groups does not admit a faithful $m$-transitive representation.

Keywords: $m$-group, Cartesian product, $m$-transitive representation of an $m$-group.

UDC: 512.545

MSC: Primary 06F15; Secondary 08B15

Received: 28.12.2021
Accepted: June 1, 2023

DOI: 10.17223/19988621/83/2