Divisible Rigid Groups. IV. Definable Subgroups Full article
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Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302 |
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| Output data | Year: 2020, Volume: 59, Number: 3, Pages: 237-252 Pages count : 16 DOI: 10.1007/s10469-020-09596-7 | ||||
| Tags | definable subgroup; divisible group; rigid group | ||||
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Abstract:
A group G is said to be rigid if it contains a normal series G = G1 > G2 > … > Gm > Gm+1 = 1, whose quotients Gi/Gi+1 are Abelian and, when treated as right ℤ[G/Gi]-modules, are torsion-free. A rigid group G is divisible if elements of the quotient Gi/Gi+1 are divisible by nonzero elements of the ring ℤ[G/Gi]. We describe subgroups of a divisible rigid group which are definable in the signature of the theory of groups without parameters and with parameters. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.
Cite:
Romanovskii N.S.
Divisible Rigid Groups. IV. Definable Subgroups
Algebra and Logic. 2020. V.59. N3. P.237-252. DOI: 10.1007/s10469-020-09596-7 WOS Scopus OpenAlex
Divisible Rigid Groups. IV. Definable Subgroups
Algebra and Logic. 2020. V.59. N3. P.237-252. DOI: 10.1007/s10469-020-09596-7 WOS Scopus OpenAlex
Identifiers:
| Web of science: | WOS:000585009100004 |
| Scopus: | 2-s2.0-85094635251 |
| OpenAlex: | W3096865134 |