Standard

Characterization of finitely generated groups by types. / Myasnikov, A. G.; Romanovskii, N. S.

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

Research output: Contribution to journal › Article › peer-review

Harvard

Myasnikov, AG & Romanovskii, NS 2018, 'Characterization of finitely generated groups by types', International Journal of Algebra and Computation, vol. 28, no. 8, pp. 1613-1632. https://doi.org/10.1142/S0218196718400118

APA

Myasnikov, A. G., & Romanovskii, N. S. (2018). Characterization of finitely generated groups by types. International Journal of Algebra and Computation, 28(8), 1613-1632. https://doi.org/10.1142/S0218196718400118

Vancouver

Myasnikov AG, Romanovskii NS. Characterization of finitely generated groups by types. International Journal of Algebra and Computation. 2018 Dec 1;28(8):1613-1632. doi: 10.1142/S0218196718400118

Author

Myasnikov, A. G. ; Romanovskii, N. S. / Characterization of finitely generated groups by types. In: International Journal of Algebra and Computation. 2018 ; Vol. 28, No. 8. pp. 1613-1632.

BibTeX

@article{0d44418b461746aa818ed8a6f80a3d10,
title = "Characterization of finitely generated groups by types",
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.",
keywords = "elementary embedding, free, Group, metabelian, nilpotent, type, ELEMENTARY THEORY, GEOMETRY",
author = "Myasnikov, {A. G.} and Romanovskii, {N. S.}",
year = "2018",
month = dec,
day = "1",
doi = "10.1142/S0218196718400118",
language = "English",
volume = "28",
pages = "1613--1632",
journal = "International Journal of Algebra and Computation",
issn = "0218-1967",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "8",

}

RIS

TY - JOUR

T1 - Characterization of finitely generated groups by types

AU - Myasnikov, A. G.

AU - Romanovskii, N. S.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

AB - 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.

KW - elementary embedding

KW - free

KW - Group

KW - metabelian

KW - nilpotent

KW - type

KW - ELEMENTARY THEORY

KW - GEOMETRY

UR - http://www.scopus.com/inward/record.url?scp=85054823530&partnerID=8YFLogxK

U2 - 10.1142/S0218196718400118

DO - 10.1142/S0218196718400118

M3 - Article

AN - SCOPUS:85054823530

VL - 28

SP - 1613

EP - 1632

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

SN - 0218-1967

IS - 8

ER -

ID: 17119549