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This article is cited in 7 scientific papers (total in 7 papers)
Divisible rigid groups. IV. Definable subgroups
N. S. Romanovskiiab a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Abstract:
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.
Keywords:
rigid group, divisible group, definable subgroup.
Received: 08.10.2019 Revised: 21.10.2020
Citation:
N. S. Romanovskii, “Divisible rigid groups. IV. Definable subgroups”, Algebra Logika, 59:3 (2020), 344–366; Algebra and Logic, 59:3 (2020), 237–252
Linking options:
https://www.mathnet.ru/eng/al2619 https://www.mathnet.ru/eng/al/v59/i3/p344
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Abstract page: | 180 | Full-text PDF : | 17 | References: | 24 | First page: | 6 |
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