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Generalized Rigid Groups: Definitions, Basic Properties, and Problems

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Abstract

We find a natural generalization of the concept of rigid group. The generalized rigid groups are also called r-groups. The terms of the corresponding rigid series of every r-group can be characterized by both ∃-formulas and ∀-formulas. We find a recursive system of axioms for the class of r-groups of fixed solubility length. We define divisible r-groups and give an appropriate system of axioms. Several fundamental problems are stated.

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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

Original Russian Text © 2018 Romanovskii N.S.

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, vol. 59, no. 4, pp. 891–896, July–August, 2018; DOI: 10.17377/smzh.2018.59.412.

The author was supported by the Russian Science Foundation (Grant 14–21–00065).

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Romanovskii, N.S. Generalized Rigid Groups: Definitions, Basic Properties, and Problems. Sib Math J 59, 705–709 (2018). https://doi.org/10.1134/S0037446618040122

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  • DOI: https://doi.org/10.1134/S0037446618040122

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