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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 5, Pages 883–924 (Mi izv1540)  

This article is cited in 6 scientific papers (total in 6 papers)

A finitely generated complete group

V. S. Guba


Abstract: An example of a $2$-generated complete group (different from the identity) with unique extraction of roots is constructed. An example is indicated, in passing, of a noncyclic $2$-generated group in which every element is conjugate to some power of a fixed element. It is proved that there are continuum many nonisomorphic such examples. The proof is based on a method developed in several papers of A. Yu. Ol'shanskii.
Bibliography: 8 titles.

Full text: PDF file (5495 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1987, 29:2, 233–277

Bibliographic databases:

UDC: 512.543
MSC: 20F05
Received: 19.04.1984

Citation: V. S. Guba, “A finitely generated complete group”, Izv. Akad. Nauk SSSR Ser. Mat., 50:5 (1986), 883–924; Math. USSR-Izv., 29:2 (1987), 233–277

Citation in format AMSBIB
\Bibitem{Gub86}
\by V.~S.~Guba
\paper A~finitely generated complete group
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 5
\pages 883--924
\mathnet{http://mi.mathnet.ru/izv1540}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=873654}
\zmath{https://zbmath.org/?q=an:0631.20025}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 29
\issue 2
\pages 233--277
\crossref{https://doi.org/10.1070/IM1987v029n02ABEH000969}


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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. V. D. Mazurov, “Solved problems in the Kourovka Notebook”, Russian Math. Surveys, 46:5 (1991), 137–182  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. S. I. Adian, “The Burnside Problem on Periodic Groups, and Related Problems”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S2–S12  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. I. A. Taimanov, “The type numbers of closed geodesics”, Reg Chaot Dyn, 15:1 (2010), 84  crossref  isi  elib
    4. 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
    5. Eric Jespers, David Riley, “Behaviour of the Frobenius map in a noncommutative world”, Journal of Algebra, 438 (2015), 7  crossref
    6. S. I. Adian, V. S. Atabekyan, “Central extensions of free periodic groups”, Sb. Math., 209:12 (2018), 1677–1689  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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