Generic Types and Generic Elements in Divisible Rigid Groups

A. G. Myasnikov, N. S. Romanovskii

Research output: Contribution to journalArticlepeer-review

Abstract

A group G is said to be m-rigid if it contains a normal series of the form G = G 1 > G 2 >.. > Gm > Gm+1 = 1, whose quotients Gi/Gi+1 are Abelian and, treated as (right) ℤ[G/Gi]-modules, are torsion-free. A rigid group G is said to be divisible if elements of the quotient ρi(G)/ρi+1(G) are divisible by nonzero elements of the ring ℤ[G/ρi(G)]. Previously, it was proved that the theory of divisible m-rigid groups is complete and ω-stable. In the present paper, we give an algebraic description of elements and types that are generic over a divisible m-rigid group G.

Original languageEnglish
Pages (from-to)72-79
Number of pages8
JournalAlgebra and Logic
Volume62
Issue number1
DOIs
StatePublished - Mar 2023

Keywords

  • divisible m-rigid group
  • generic element
  • generic type

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