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Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 2, Pages 309–321 (Mi izv1668)  

This article is cited in 22 scientific papers (total in 22 papers)

An infinite group with subgroups of prime orders

A. Yu. Ol'shanskii


Abstract: An infinite nonabelian group all of whose proper subgroups have prime order is constructed. This solves a problem of O. Yu. Schmidt. The proof involves modifying and extending the series of lemmas in an earlier paper of the author.
Bibliography: 3 titles.

Full text: PDF file (1413 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1981, 16:2, 279–289

Bibliographic databases:

UDC: 512
MSC: Primary 20F10; Secondary 03D40
Received: 20.12.1978

Citation: A. Yu. Ol'shanskii, “An infinite group with subgroups of prime orders”, Izv. Akad. Nauk SSSR Ser. Mat., 44:2 (1980), 309–321; Math. USSR-Izv., 16:2 (1981), 279–289

Citation in format AMSBIB
\Bibitem{Ols80}
\by A.~Yu.~Ol'shanskii
\paper An infinite group with subgroups of prime orders
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 2
\pages 309--321
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=571100}
\zmath{https://zbmath.org/?q=an:0475.20025}
\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 16
\issue 2
\pages 279--289
\crossref{https://doi.org/10.1070/IM1981v016n02ABEH001307}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MK40900004}


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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, “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
    2. Ragmar Rudolph, “Ein Untergruppensatz für modulare Gruppen”, Mh Math, 94:2 (1982), 149  crossref  mathscinet  zmath
    3. A. Yu. Ol'shanskii, “On the Novikov–Adyan theorem”, Math. USSR-Sb., 46:2 (1983), 203–236  mathnet  crossref  mathscinet  zmath
    4. Yu. I. Merzlyakov, “The group theory problems of the Kourovka Notebook – progress from the sixth to the seventh symposium”, Russian Math. Surveys, 37:2 (1982), 165–191  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. G. S. Deryabina, “On infinite $p$-groups with cyclic subgroups”, Math. USSR-Sb., 52:2 (1985), 481–490  mathnet  crossref  mathscinet  zmath
    6. M. Kuzucuoǧlu, “Barely transitive permutation groups”, Arch Math, 55:6 (1990), 521  crossref  mathscinet  zmath  isi
    7. V. V. Butakov, L. M. Martynov, “Semigroups all of whose noncyclic subsemigroups are ideals”, Russian Math. (Iz. VUZ), 42:11 (1998), 90–92  mathnet  mathscinet  zmath  elib
    8. V. I. Senashov, A. I. Sozutov, V. P. Shunkov, “Investigation of groups with finiteness conditions in Krasnoyarsk”, Russian Math. Surveys, 60:5 (2005), 805–848  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. N. S. Chernikov, “Groups with minimal conditions”, J. Math. Sci., 163:6 (2009), 774–784  mathnet  crossref  mathscinet  elib
    10. 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
    11. Jon González-Sánchez, Benjamin Klopsch, “On w-maximal groups”, Journal of Algebra, 328:1 (2011), 155  crossref
    12. Aladova E., Plotkin B., “Varieties of Representations of Groups and Varieties of Associative Algebras”, Internat J Algebra Comput, 21:7 (2011), 1149–1178  crossref  isi
    13. Eberhard Kaniuth, Ali Ülger, “The structure of power bounded elements in Fourier–Stieltjes algebras of locally compact groups”, Bulletin des Sciences Mathématiques, 2012  crossref
    14. N. S. Chernikov, “Three S. N. Chernikov's questions”, Tr. IMM UrO RAN, 18, no. 3, 2012, 23–25  mathnet  elib
    15. Ershov M., “Golod-Shafarevich Groups: a Survey”, Int. J. Algebr. Comput., 22:5 (2012), 1230001  crossref  isi
    16. E. V. Mescherina, “O razlichnykh opredeleniyakh artinovosti dlya algebr Li”, Chebyshevskii sb., 14:3 (2013), 75–80  mathnet
    17. 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
    18. M. G. Benli, R. I. Grigorchuk, T. V. Nagnibeda, “Universal Groups of Intermediate Growth and Their Invariant Random Subgroups”, Funct. Anal. Appl., 49:3 (2015), 159–174  mathnet  crossref  crossref  isi  elib
    19. Anatoliy I. Sozutov, Inna O. Aleksandrova, “On some properties of adjoint groups of associative nil algebras”, Zhurn. SFU. Ser. Matem. i fiz., 10:4 (2017), 503–508  mathnet  crossref
    20. A. I. Sozutov, E. B. Durakov, “On groups with a Frobenius element”, Siberian Math. J., 59:5 (2018), 938–946  mathnet  crossref  crossref  isi
    21. E. V. Mescherina, O. A. Pikhtilkova, “Razvitie ponyatiya «artinovost» dlya algebr Li”, Chebyshevskii sb., 19:1 (2018), 167–175  mathnet  crossref  elib
    22. D. N. Azarov, N. S. Romanovskii, “O konechnykh gomomorfnykh obrazakh grupp konechnogo ranga”, Sib. matem. zhurn., 60:3 (2019), 483–488  mathnet  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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