Geodesic
Divisible rigid groups. IV. Definable subgroups
Algebra i logika, Tome 59 (2020) no. 3, pp. 344-366.

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

A group $G$ is said to be rigid if it contains a normal series $$G=G_1>G_2>\ldots>G_m>G_{m+1}=1,$$ whose quotients $G_i/G_{i+1}$ are Abelian and, when treated as right $\mathbb{Z} [G/G_i]$-modules, are torsion-free. A rigid group $G$ is divisible if elements of the quotient $G_i/G_{i+1}$ are divisible by nonzero elements of the ring $\mathbb{Z} [G/G_i]$. We describe subgroups of a divisible rigid group which are definable in the signature of the theory of groups without parameters and with parameters.
Mots-clés : rigid group, divisible group
Keywords: definable subgroup. 
@article{AL_2020_59_3_a5,
     author = {N. S. Romanovskii},
     title = {Divisible rigid groups. {IV.} {Definable} subgroups},
     journal = {Algebra i logika},
     pages = {344--366},
     publisher = {mathdoc},
     volume = {59},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2020_59_3_a5/}
}
TY  - JOUR
AU  - N. S. Romanovskii
TI  - Divisible rigid groups. IV. Definable subgroups
JO  - Algebra i logika
PY  - 2020
SP  - 344
EP  - 366
VL  - 59
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2020_59_3_a5/
LA  - ru
ID  - AL_2020_59_3_a5
ER  - 
%0 Journal Article
%A N. S. Romanovskii
%T Divisible rigid groups. IV. Definable subgroups
%J Algebra i logika
%D 2020
%P 344-366
%V 59
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2020_59_3_a5/
%G ru
%F AL_2020_59_3_a5
N. S. Romanovskii. Divisible rigid groups. IV. Definable subgroups. Algebra i logika, Tome 59 (2020) no. 3, pp. 344-366. http://geodesic.mathdoc.fr/item/AL_2020_59_3_a5/

[1] N. S. Romanovskii, “Delimye zhestkie gruppy. Algebraicheskaya zamknutost i elementarnaya teoriya”, Algebra i logika, 56:5 (2017), 593–612 | MR | Zbl

[2] A. G. Myasnikov, N. S. Romanovskii, “Delimye zhestkie gruppy. II. Stabilnost, nasyschennost i elementarnye podmodeli”, Algebra i logika, 57:1 (2018), 43–56 | MR | Zbl

[3] N. S. Romanovskii, “Delimye zhestkie gruppy. III. Odnorodnost i eliminatsiya kvantorov”, Algebra i logika, 57:6 (2018), 733–748 | MR

[4] N. S. Romanovskii, “Neterovost po uravneniyam zhestkikh razreshimykh grupp”, Algebra i logika, 48:2 (2009), 258–279 | MR | Zbl

[5] N. S. Romanovskii, “Neprivodimye algebraicheskie mnozhestva nad delimymi raspavshimisya zhestkimi gruppami”, Algebra i logika, 48:6 (2009), 793–818 | MR | Zbl

[6] N. S. Romanovskii, “O neprivodimosti affinnogo prostranstva v algebraicheskoi geometrii nad gruppoi”, Algebra i logika, 52:3 (2013), 386–391 | MR | Zbl

[7] Yu. L. Ershov, E. A. Palyutin, Matematicheskaya logika, 6-e izd., Fizmatlit, M., 2011 | MR