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Sibirsk. Mat. Zh., 2003, Volume 44, Number 2, Pages 438–443 (Mi smj1187)  

This article is cited in 5 scientific papers (total in 5 papers)

On some elementary properties of soluble groups of derived length 2

N. S. Romanovskiia, E. I. Timoshenkob

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University of Architecture and Civil Engineering

Abstract: Conditions are found for a soluble group of derived length 2 with few relations to be universally equivalent to a free soluble group of derived length 2. The Fitting radical of a soluble group of derived length 2 with few relations coincides with the derived subgroup. Also, if an $n$-generator soluble group is elementarily equivalent to a free soluble group of rank $m$ and derived length $k$ then for $k=2$ or $k>2$ and $n=m$ the groups are isomorphic.

Keywords: group, soluble, derived subgroup, elementary theory

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English version:
Siberian Mathematical Journal, 2003, 44:2, 350–354

Bibliographic databases:

UDC: 512.5
Received: 16.12.2002

Citation: N. S. Romanovskii, E. I. Timoshenko, “On some elementary properties of soluble groups of derived length 2”, Sibirsk. Mat. Zh., 44:2 (2003), 438–443; Siberian Math. J., 44:2 (2003), 350–354

Citation in format AMSBIB
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\by N.~S.~Romanovskii, E.~I.~Timoshenko
\paper On some elementary properties of soluble groups of derived length 2
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
\issue 2
\pages 438--443
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1981379}
\zmath{https://zbmath.org/?q=an:1033.20034}
\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 2
\pages 350--354
\crossref{https://doi.org/10.1023/A:1022949224145}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000182502000017}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. I. Budkin, “Quasivariety Generated by Free Metabelian and 2-Nilpotent Groups”, Algebra and Logic, 44:4 (2005), 213–218  mathnet  crossref  mathscinet  zmath
    2. Khelif A., “Bi–interpretability and QFA structures: study of some soluble groups and commutative rings”, Comptes Rendus Mathematique, 345:2 (2007), 59–61  crossref  mathscinet  zmath  isi  scopus
    3. E. I. Timoshenko, “On splittings, subgroups, and theories of partially commutative metabelian groups”, Siberian Math. J., 59:3 (2018), 536–541  mathnet  crossref  crossref  isi  elib
    4. E. I. Timoshenko, “Theories of relatively free solvable groups with extra predicate”, Algebra and Logic, 57:4 (2018), 295–308  mathnet  crossref  crossref  isi
    5. N. S. Romanovskii, E. I. Timoshenko, “Ob elementarnoi ekvivalentnosti i pryamykh razlozheniyakh chastichno kommutativnykh grupp mnogoobrazii”, Sib. matem. zhurn., 61:3 (2020), 681–686  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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