Characterization of finitely generated groups by types

A. G. Myasnikov, N. S. Romanovskii

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this paper we show that all finitely generated nilpotent, metabelian, polycyclic, and rigid (hence free solvable) groups G are fully characterized in the class of all groups by the set tp(G) of types realized in G. Furthermore, it turns out that these groups G are fully characterized already by some particular rather restricted fragments of the types from tp(G). In particular, every finitely generated nilpotent group is completely defined by its +-types, while a finitely generated rigid group is completely defined by its types, and a finitely generated metabelian or polycyclic group is completely defined by its -types. We have similar results for some non-solvable groups: free, surface, and free Burnside groups, though they mostly serve as illustrations of general techniques or provide some counterexamples.

Original languageEnglish
Pages (from-to)1613-1632
Number of pages20
JournalInternational Journal of Algebra and Computation
Volume28
Issue number8
DOIs
Publication statusPublished - 1 Dec 2018

Keywords

  • elementary embedding
  • free
  • Group
  • metabelian
  • nilpotent
  • type
  • ELEMENTARY THEORY
  • GEOMETRY

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