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Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 6, Pages 1328–1393 (Mi izv1758)  

This article is cited in 14 scientific papers (total in 14 papers)

An infinite simple Noetherian group without torsion

A. Yu. Ol'shanskii


Abstract: The well-known Baer conjecture on the “almost polycyclicity” of any Noetherian group is refuted; an example is constructed in terms of generators and defining relations. A complicated simultaneous induction on rank is based on a geometric interpretation of the deducibility of relations from defining relations.
Bibliography: 6 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1980, 15:3, 531–588

Bibliographic databases:

UDC: 512
MSC: Primary 20E15; Secondary 20F05, 20E32
Received: 24.10.1978

Citation: A. Yu. Ol'shanskii, “An infinite simple Noetherian group without torsion”, Izv. Akad. Nauk SSSR Ser. Mat., 43:6 (1979), 1328–1393; Math. USSR-Izv., 15:3 (1980), 531–588

Citation in format AMSBIB
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\paper An infinite simple Noetherian group without torsion
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\yr 1979
\vol 43
\issue 6
\pages 1328--1393
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\zmath{https://zbmath.org/?q=an:0453.20024|0431.20027}
\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 15
\issue 3
\pages 531--588
\crossref{https://doi.org/10.1070/IM1980v015n03ABEH001268}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Yu. Ol'shanskii, “An infinite group with subgroups of prime orders”, Math. USSR-Izv., 16:2 (1981), 279–289  mathnet  crossref  mathscinet  zmath  isi
    2. A. Yu. Ol'shanskii, “On the problem of the existence of an invariant mean on a group”, Russian Math. Surveys, 35:4 (1980), 180–181  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. A. Yu. Ol'shanskii, “On the Novikov–Adyan theorem”, Math. USSR-Sb., 46:2 (1983), 203–236  mathnet  crossref  mathscinet  zmath
    4. Stephen J. Pride, “Some finitely presented groups of cohomological dimension two with property (FA)”, Journal of Pure and Applied Algebra, 29:2 (1983), 167  crossref
    5. G. S. Deryabina, “On infinite $p$-groups with cyclic subgroups”, Math. USSR-Sb., 52:2 (1985), 481–490  mathnet  crossref  mathscinet  zmath
    6. A. Yu. Ol'shanskii, “Periodic factor of hyperbolic groups”, Math. USSR-Sb., 72:2 (1992), 519–541  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. B. P. Vankov, “Ob elementakh $T(6)-1/3$-grupp”, Chebyshevskii sb., 3:1 (2002), 32–34  mathnet  mathscinet  zmath
    8. Thomas S., “On the complexity of the quasi-isometry and virtual isomorphism problems for finitely generated groups”, Groups Geometry and Dynamics, 2:2 (2008), 281–307  isi
    9. S. I. Adian, “The Burnside problem and related topics”, Russian Math. Surveys, 65:5 (2010), 805–855  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. M. Filali, M. Neufang, M. Sangani Monfared, “Weak factorizations of operators in the group von Neumann algebras of certain amenable groups and applications”, Math Ann, 2010  crossref
    11. R. I. Grigorchuk, “Some topics in the dynamics of group actions on rooted trees”, Proc. Steklov Inst. Math., 273 (2011), 64–175  mathnet  crossref  mathscinet  zmath  isi  elib
    12. Nikolai S. Chernikov, “Groups satisfying the minimal condition for non-abelian non-normal subgroups”, Zhurn. SFU. Ser. Matem. i fiz., 7:1 (2014), 22–34  mathnet
    13. Nikolai S. Chernikov, “Some minimal conditions in certain extremely large classes of groups”, Zhurn. SFU. Ser. Matem. i fiz., 8:1 (2015), 22–27  mathnet
    14. S. I. Adian, “New estimates of odd exponents of infinite Burnside groups”, Proc. Steklov Inst. Math., 289 (2015), 33–71  mathnet  crossref  crossref  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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