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Izv. Akad. Nauk SSSR Ser. Mat., 1968, Volume 32, Issue 5, Pages 1176–1190 (Mi izv2512)  

This article is cited in 11 scientific papers (total in 12 papers)

On abelian subgroups and the conjugacy problem in free periodic groups of odd order

P. S. Novikov, S. I. Adian


Abstract: We prove the finiteness of any abelian subgroup of a free periodic group of odd order $n \geqslant4381$. We also show that for these groups the conjugacy problem is solvable.

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English version:
Mathematics of the USSR-Izvestiya, 1968, 2:5, 1131–1144

Bibliographic databases:

Document Type: Article
UDC: 519.4
MSC: 20K27, 20E45, 20F50, 20F10
Received: 06.05.1968

Citation: P. S. Novikov, S. I. Adian, “On abelian subgroups and the conjugacy problem in free periodic groups of odd order”, Izv. Akad. Nauk SSSR Ser. Mat., 32:5 (1968), 1176–1190; Math. USSR-Izv., 2:5 (1968), 1131–1144

Citation in format AMSBIB
\Bibitem{NovAdi68}
\by P.~S.~Novikov, S.~I.~Adian
\paper On abelian subgroups and the conjugacy problem in free periodic
groups of odd order
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1968
\vol 32
\issue 5
\pages 1176--1190
\mathnet{http://mi.mathnet.ru/izv2512}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=233876}
\zmath{https://zbmath.org/?q=an:0204.34102}
\transl
\jour Math. USSR-Izv.
\yr 1968
\vol 2
\issue 5
\pages 1131--1144
\crossref{https://doi.org/10.1070/IM1968v002n05ABEH000722}


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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. S. I. Adian, “On some torsion-free groups”, Math. USSR-Izv., 5:3 (1971), 475–484  mathnet  crossref  mathscinet  zmath
    2. S. I. Adian, “An axiomatic method of constructing groups with given properties”, Russian Math. Surveys, 32:1 (1977), 1–14  mathnet  crossref  mathscinet  zmath
    3. V. D. Mazurov, “Solved problems in the Kourovka Notebook”, Russian Math. Surveys, 46:5 (1991), 137–182  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. S. I. Adian, V. G. Durnev, “Decision problems for groups and semigroups”, Russian Math. Surveys, 55:2 (2000), 207–296  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. 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
    6. 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
    7. 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
    8. V. S. Atabekyan, “The normalizers of free subgroups in free Burnside groups of odd period $n\ge1003$”, J. Math. Sci., 166:6 (2010), 691–703  mathnet  crossref  mathscinet  elib
    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. V. S. Atabekyan, “Normal automorphisms of free Burnside groups”, Izv. Math., 75:2 (2011), 223–237  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. V. S. Atabekyan, “On normal subgroups in the periodic products of S. I. Adian”, Proc. Steklov Inst. Math., 274 (2011), 9–24  mathnet  crossref  mathscinet  isi
    12. 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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