On metabelian groups with derived quotient an elementary abelian $2$-group of rank $3$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 361-375
Citer cet article
Voir la notice de l'article provenant de la source Math-Net.Ru
Necessary and sufficient conditions in terms of rank and exponent for the existence of torsion-free metabelian groups with derived quotient an elementary abelian $p$-group of rank $k$ are formulated.
[1] Furtwängler Ph., “Beweis der Hauptidealsatzes für den Klassenkörper algebraischer Zahlkörper”, Abh. Math. Sem. Hamburg. Univ., 7 (1930), 14–36
[2] Gupta N., Sidki S., “On torsion-free metabelian groups with commutator quotients of prime exponent”, Int. Journal of Algebra and Computation, 9 (1999), 493–520 | DOI | MR | Zbl
[3] Kopytov V. M., Medvedev N. Ya., Right ordered groups, Plenum Pub. Co., 1996 | MR
[4] Mura R. B., Rhemtulla A. H., Orderable Groups, Marcel Dekker, 1977 | MR
[5] Smirnov D. M., “One-sided orders on groups with ascending central series”, Algebra i logika, 6:2 (1967), 77–88 (Russian) | MR