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Divisible Rigid Groups. IV. Definable Subgroups

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Algebra and Logic Aims and scope

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.

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References

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia

    N. S. Romanovskii

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  1. N. S. Romanovskii
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Correspondence to N. S. Romanovskii.

Additional information

Translated from Algebra i Logika, Vol. 59, No. 3, pp. 344-366, May-June, 2020. Russian https://doi.org/10.33048/alglog.2020.59.305.

N. S. Romanovskii is supported by Russian Science Foundation, project No. 19-11-00039.

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Romanovskii, N.S. Divisible Rigid Groups. IV. Definable Subgroups. Algebra Logic 59, 237–252 (2020). https://doi.org/10.1007/s10469-020-09596-7

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  • DOI: https://doi.org/10.1007/s10469-020-09596-7

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