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Mat. Sb. (N.S.), 1982, Volume 118(160), Number 2(6), Pages 203–235 (Mi msb2249)  

This article is cited in 13 scientific papers (total in 14 papers)

On the Novikov–Adyan theorem

A. Yu. Ol'shanskii


Abstract: A new solution of the restricted Burnside problem for sufficiently large odd exponents is presented. The proof is considerably shorter than the original one given by P. S. Novikov and S. I. Adyan in 1968 (although the bound for the exponent is worse: $n>10^{10}$). It is based on a geometrical interpretation of deducibility of relations in a group from its defining relations.
Figures: 16.
Bibliography: 7 titles.

Full text: PDF file (2057 kB)
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English version:
Mathematics of the USSR-Sbornik, 1983, 46:2, 203–236

Bibliographic databases:

UDC: 512
MSC: 20E05, 20F05
Received: 06.04.1981

Citation: A. Yu. Ol'shanskii, “On the Novikov–Adyan theorem”, Mat. Sb. (N.S.), 118(160):2(6) (1982), 203–235; Math. USSR-Sb., 46:2 (1983), 203–236

Citation in format AMSBIB
\Bibitem{Ols82}
\by A.~Yu.~Ol'shanskii
\paper On the Novikov--Adyan theorem
\jour Mat. Sb. (N.S.)
\yr 1982
\vol 118(160)
\issue 2(6)
\pages 203--235
\mathnet{http://mi.mathnet.ru/msb2249}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=658789}
\zmath{https://zbmath.org/?q=an:0539.20020}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 46
\issue 2
\pages 203--236
\crossref{https://doi.org/10.1070/SM1983v046n02ABEH002768}


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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, “Varieties in which all finite groups are Abelian”, Math. USSR-Sb., 54:1 (1986), 57–80  mathnet  crossref  mathscinet  zmath
    2. V. S. Guba, “A finitely generated complete group”, Math. USSR-Izv., 29:2 (1987), 233–277  mathnet  crossref  mathscinet  zmath
    3. Atabekian V., “On Simple and Free Periodical Groups”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1987, no. 6, 76–78  mathscinet  isi
    4. V. N. Obraztsov, “An imbedding theorem for groups and its corollaries”, Math. USSR-Sb., 66:2 (1990), 541–553  mathnet  crossref  mathscinet  zmath  isi
    5. I. G. Lysenok, “Infinite Burnside groups of even exponent”, Izv. Math., 60:3 (1996), 453–654  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Ivanov, SV, “Embedding free Burnside groups in finitely presented groups”, Geometriae Dedicata, 111:1 (2005), 87  crossref  isi
    7. Ivanov S. Storozhev A., “Non-Hopfian Relatively Free Groups”, Geod. Dedic., 114:1 (2005), 209–228  crossref  mathscinet  zmath  isi
    8. L. D. Beklemishev, I. G. Lysenok, A. A. Mal'tsev, S. P. Novikov, M. R. Pentus, A. A. Razborov, A. L. Semenov, V. A. Uspenskii, “Sergei Ivanovich Adian (on his 75th birthday)”, Russian Math. Surveys, 61:3 (2006), 575–588  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. Delzant T., Gromov M., “Curvature Theory of Mesoscopic and the Tiny Simplification”, J. Topol., 1:4 (2008), 804–836  crossref  mathscinet  zmath  isi
    10. Grigorchuk, RI, “ON DEHN FUNCTIONS OF INFINITE PRESENTATIONS OF GROUPS”, Geometric and Functional Analysis, 18:6 (2009), 1841  crossref  isi  elib
    11. A. S. Pahlevanyan, “Infinite order automorphisms of free periodic groups of sufficiently large exponent”, Uch. zapiski EGU, ser. Fizika i Matematika, 2009, no. 2, 38–42  mathnet
    12. 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
    13. Coulon R., “Growth of Periodic Quotients of Hyperbolic Groups”, Algebr. Geom. Topol., 13:6 (2013), 3111–3133  crossref  isi
    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
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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