Characterization of finitely generated groups by types

Alexei Miasnikov, N. S. Romanovskii

Research output: Contribution to journalArticle

1 Citation (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 (US)
Pages (from-to)1613-1632
Number of pages20
JournalInternational Journal of Algebra and Computation
Volume28
Issue number8
DOIs
StatePublished - Dec 1 2018

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Finitely Generated Group
Finitely Generated
Polycyclic Group
Metabelian group
Solvable Group
Nilpotent Group
Free Group
Free Surface
Counterexample
Fragment

Cite this

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Characterization of finitely generated groups by types. / Miasnikov, Alexei; Romanovskii, N. S.

In: International Journal of Algebra and Computation, Vol. 28, No. 8, 01.12.2018, p. 1613-1632.

Research output: Contribution to journalArticle

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