Geodesic
Completion of Linearly Ordered Metabelian Groups
Algebra i logika, Tome 42 (2003) no. 5, pp. 542-565.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove a theorem saying that in finitely generated linearly ordered metabelian groups there exists a finite system of normal convex subgroups satisfying orderability conditions for groups, and an embedding theorem for linearly ordered metabelian groups whose initial linear orders extend to $\Gamma$-divisible linearly ordered metabelian ones. As a consequence, it is stated that orderable metabelian groups are embedded, with extension of all their linear orders, in $\Gamma$-divisible orderable metabelian groups.
Keywords: linearly ordered metabelian group, $Gamma$-divisible linearly ordered metabelian group, normal convex subgroup. 
@article{AL_2003_42_5_a1,
     author = {V. V. Bludov},
     title = {Completion of {Linearly} {Ordered} {Metabelian} {Groups}},
     journal = {Algebra i logika},
     pages = {542--565},
     publisher = {mathdoc},
     volume = {42},
     number = {5},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2003_42_5_a1/}
}
TY  - JOUR
AU  - V. V. Bludov
TI  - Completion of Linearly Ordered Metabelian Groups
JO  - Algebra i logika
PY  - 2003
SP  - 542
EP  - 565
VL  - 42
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2003_42_5_a1/
LA  - ru
ID  - AL_2003_42_5_a1
ER  - 
%0 Journal Article
%A V. V. Bludov
%T Completion of Linearly Ordered Metabelian Groups
%J Algebra i logika
%D 2003
%P 542-565
%V 42
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2003_42_5_a1/
%G ru
%F AL_2003_42_5_a1
V. V. Bludov. Completion of Linearly Ordered Metabelian Groups. Algebra i logika, Tome 42 (2003) no. 5, pp. 542-565. http://geodesic.mathdoc.fr/item/AL_2003_42_5_a1/

[1] A. I. Maltsev, “Nilpotentnye gruppy bez krucheniya”, Izv. AN SSSR, ser. matem., 13:3 (1949), 201–212

[2] A. I. Kokorin, V. M. Kopytov, Lineino uporyadochennye gruppy, Nauka, M., 1972 | MR | Zbl

[3] V. V. Bludov, N. Ya. Medvedev, “O popolnenii uporyadochivaemykh metabelevykh grupp”, Algebra i logika, 13:4 (1974), 369–373 | MR | Zbl

[4] M. I. Kargapolov, Yu. I. Merzlyakov, Osnovy teorii grupp, Nauka, M., 1996 | MR | Zbl

[5] V. M. Kopytov, Reshetochno uporyadochennye gruppy, Nauka, M., 1984 | MR | Zbl

[6] V. M. Kopytov, N. Ya. Medvedev, Pravouporyadochennye gruppy, Sibirskaya shkola algebry i logiki, Nauchnaya kniga (NII MIOO NGU), Novosibirsk, 1996 | MR | Zbl

[7] A. G. Kurosh, Teoriya grupp, Nauka, M., 1967 | MR | Zbl

[8] A. I. Kokorin, “O douporyadochivaemykh gruppakh”, Dokl. AN SSSR, 151:1 (1963), 31–33 | MR | Zbl

[9] A. I. Maltsev, “Ob uporyadochennykh gruppakh”, Izv. AN SSSR, ser. matem., 13:6 (1949), 473–482

[10] V. D. Podderyugin, “Uslovie uporyadochivaemosti gruppy”, Izv. AN SSSR, ser. matem., 21:2 (1957), 199–208 | MR

[11] L. S. Rieger, “On the ordered and cyclically ordered groups (I-III)”, Vĕstn. Kral. C̆s. Spolec̆ Nauk, 6 (1946), 1–31 ; 1 (1947), 1–33; 1 (1948), 1–26 | MR | MR

[12] L. Kaloujnine, M. Krasner, “Produit complet des group de permutation et problém d'extension des groupes. I, II”, Acta Sci. Math., 13 (1950), 208–230 ; 14 (1951), 39–66 | MR | Zbl | MR | Zbl

[13] C. Fox, “An embedding theorem for ordered groups”, Bull. Aust. Math. Soc., 12:3 (1975), 321–335 | DOI | MR | Zbl

[14] V. M. Kopytov, “O lineino uporyadochennykh razreshimykh gruppakh”, Algebra i logika, 12:6 (1973), 655–666 | MR | Zbl

[15] A. I. Kokorin, “K teorii douporyadochivaemykh grupp”, Algebra i logika, 2:6 (1963), 15–20 | MR | Zbl

[16] A. I. Maltsev, Algebraicheskie sistemy, Nauka, M., 1970 | MR

[17] Spravochnaya kniga po matematicheskoi logike, ch. 1: Teoriya modelei, ed. Dzh. Barvaisa, Nauka, M., 1982 | MR