Generalized Rigid Groups: Definitions, Basic Properties, and Problems

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2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)705-709
Number of pages5
JournalSiberian Mathematical Journal
Issue number4
Publication statusPublished - 1 Jul 2018


  • divisible group
  • group axioms
  • soluble group

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