On metabelian groups with derived quotient an elementary abelian $2$-group of rank $3$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 361-375
Cet article a éte moissonné depuis 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.
@article{SEMR_2007_4_a22,
author = {V. V. Bludov and L. V. Dolbak},
title = {On metabelian groups with derived quotient an elementary abelian $2$-group of rank~$3$},
journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
pages = {361--375},
year = {2007},
volume = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SEMR_2007_4_a22/}
}
TY - JOUR AU - V. V. Bludov AU - L. V. Dolbak TI - On metabelian groups with derived quotient an elementary abelian $2$-group of rank $3$ JO - Sibirskie èlektronnye matematičeskie izvestiâ PY - 2007 SP - 361 EP - 375 VL - 4 UR - http://geodesic.mathdoc.fr/item/SEMR_2007_4_a22/ LA - en ID - SEMR_2007_4_a22 ER -
V. V. Bludov; L. V. Dolbak. On metabelian groups with derived quotient an elementary abelian $2$-group of rank $3$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 361-375. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a22/
[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