Geodesic
Presentations and Cartesian product of $m$-groups
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 83 (2023), pp. 17-23 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
Mots-clés : $m$-group
Keywords: Cartesian product, $m$-transitive representation of an $m$-group. 
@article{VTGU_2023_83_a1,
     author = {A. V. Zenkov},
     title = {Presentations and {Cartesian} product of $m$-groups},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {17--23},
     year = {2023},
     number = {83},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2023_83_a1/}
}
TY  - JOUR
AU  - A. V. Zenkov
TI  - Presentations and Cartesian product of $m$-groups
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2023
SP  - 17
EP  - 23
IS  - 83
UR  - http://geodesic.mathdoc.fr/item/VTGU_2023_83_a1/
LA  - ru
ID  - VTGU_2023_83_a1
ER  - 
%0 Journal Article
%A A. V. Zenkov
%T Presentations and Cartesian product of $m$-groups
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2023
%P 17-23
%N 83
%U http://geodesic.mathdoc.fr/item/VTGU_2023_83_a1/
%G ru
%F VTGU_2023_83_a1
A. V. Zenkov. Presentations and Cartesian product of $m$-groups. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 83 (2023), pp. 17-23. http://geodesic.mathdoc.fr/item/VTGU_2023_83_a1/

[1] V. M. Kopytov, Reshetochno uporyadochennye gruppy, Nauka, M., 1984, 300 pp.

[2] M. Giraudet, J. Rachunek, “Varieties of half lattice-ordered groups of monotonic permutations of chains”, Czech. Math. J., 49 (1999), 743–766 | DOI | MR | Zbl

[3] A. I. Maltsev, Algebraicheskie sistemy, Nauka, M., 1970, 392 pp.

[4] M. Giraudet, F. Lucas, “Groupes a moitie ordonnes”, Fundam. Math., 139:2 (1991), 75–89 | DOI | MR | Zbl

[5] S. V. Varaksin, A. V. Zenkov, “On representations of m-groups”, Siberian Mathematical Journal, 54 (2013), 227–230 | DOI | MR | Zbl

[6] M. Darnel, Theory of lattice-ordered groups, Marcel Dekker, New-York, 1995, 539 pp. | Zbl