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

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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/}
}
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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/