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Izv. Akad. Nauk SSSR Ser. Mat., 1968, Volume 32, Issue 1, Pages 212–244 (Mi izv2699)  

This article is cited in 61 scientific papers (total in 63 papers)

Infinite periodic groups. I

P. S. Novikov, S. I. Adian


Abstract: In this paper we construct an example of an infinite periodic group with a finite number of generators, in which the orders of all the elements are bounded by a specified number. This is a solution of the well-known Burnside problem.

Full text: PDF file (5840 kB)

English version:
Mathematics of the USSR-Izvestiya, 1968, 2:1, 209–236

Bibliographic databases:

Document Type: Article
UDC: 519.4
MSC: 20F50, 20F05, 20F10
Received: 23.10.1967

Citation: P. S. Novikov, S. I. Adian, “Infinite periodic groups. I”, Izv. Akad. Nauk SSSR Ser. Mat., 32:1 (1968), 212–244; Math. USSR-Izv., 2:1 (1968), 209–236

Citation in format AMSBIB
\Bibitem{NovAdi68}
\by P.~S.~Novikov, S.~I.~Adian
\paper Infinite periodic groups. I
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1968
\vol 32
\issue 1
\pages 212--244
\mathnet{http://mi.mathnet.ru/izv2699}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=240178}
\zmath{https://zbmath.org/?q=an:0194.03301}
\transl
\jour Math. USSR-Izv.
\yr 1968
\vol 2
\issue 1
\pages 209--236
\crossref{https://doi.org/10.1070/IM1968v002n01ABEH000637}


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    This publication is cited in the following articles:
    1. P. S. Novikov, S. I. Adian, “Defining relations and the word problem for free periodic groups of odd order”, Math. USSR-Izv., 2:4 (1968), 935–942  mathnet  crossref  mathscinet  zmath
    2. P. S. Novikov, S. I. Adian, “On abelian subgroups and the conjugacy problem in free periodic groups of odd order”, Math. USSR-Izv., 2:5 (1968), 1131–1144  mathnet  crossref  mathscinet  zmath
    3. S. I. Adian, “Infinite irreducible systems of group identities”, Math. USSR-Izv., 4:4 (1970), 721–739  mathnet  crossref  mathscinet  zmath
    4. S. I. Adian, “On some torsion-free groups”, Math. USSR-Izv., 5:3 (1971), 475–484  mathnet  crossref  mathscinet  zmath
    5. Joseph G Rosenstein, “ℵ0-Categoricity of groups”, Journal of Algebra, 25:3 (1973), 435  crossref
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    17. S. I. Adian, A. A. Razborov, “Periodic groups and Lie algebras”, Russian Math. Surveys, 42:2 (1987), 1–81  mathnet  crossref  mathscinet  zmath  adsnasa  isi
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    23. S. I. Adian, I. G. Lysenok, “On groups all of whose proper subgroups of which are finite cyclic”, Math. USSR-Izv., 39:2 (1992), 905–957  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    24. James D. Currie, “Which graphs allow infinite nonrepetitive walks?”, Discrete Mathematics, 87:3 (1991), 249  crossref
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    29. S. I. Adian, “On the centenary of the birth of Petr Sergeevich Novikov”, Russian Math. Surveys, 56:4 (2001), 793–802  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    30. do Lago A., “Local Groups in Free Groupoids Satisfying Certain Monoid Identities”, Int. J. Algebr. Comput., 12:1-2 (2002), 357–369  crossref  isi
    31. 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
    32. LAKHDAR HAMMOUDI, “BURNSIDE AND KUROSH PROBLEMS”, Int. J. Algebra Comput, 14:02 (2004), 197  crossref
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    37. E. Aladova, B. Plotkin, “PI-groups and PI-representations of groups”, J. Math. Sci., 164:2 (2010), 155–162  mathnet  crossref  mathscinet  elib
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    50. Atabekyan V.S., “On CEP-Subgroups of n-Periodic Products”, Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences, 46:5 (2011), 237–242  isi
    51. Ershov M., “Golod-Shafarevich Groups: a Survey”, Int. J. Algebr. Comput., 22:5 (2012), 1230001  crossref  isi
    52. Lytkina D.V., “Periodic Groups with Given Properties of Finite Subgroups”, Dokl. Math., 85:1 (2012), 55–56  crossref  isi
    53. Lytkina D.V., “Periodicheskie gruppy s zadannymi svoistvami konechnykh podgrupp”, Doklady Akademii nauk, 442:3 (2012), 310–310  elib
    54. Lytkina D.V., “Gruppy s zadannymi poryadkami elementov”, Matematicheskii forum (itogi nauki. yug Rossii), 6 (2012), 85–97  elib
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    56. Atabekyan V.S., “The Groups of Automorphisms Are Complete for Free Burnside Groups of Odd Exponents N >= 1003”, Int. J. Algebr. Comput., 23:6 (2013), 1485–1496  crossref  isi
    57. F. A. Dudkin, K. S. Sviridov, “Complementing a subgroup of a hyperbolic group by a free factor”, Algebra and Logic, 52:3 (2013), 222–235  mathnet  crossref  mathscinet  isi
    58. S. I. Adian, V. S. Atabekyan, “The Hopfian Property of $n$-Periodic Products of Groups”, Math. Notes, 95:4 (2014), 443–449  mathnet  crossref  crossref  mathscinet  isi  elib
    59. Daria V. Lytkina, Victor D. Mazurov, “Groups with given element orders”, Zhurn. SFU. Ser. Matem. i fiz., 7:2 (2014), 191–203  mathnet
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    62. Coulon R. Hilion A., “Growth and Order of Automorphisms of Free Groups and Free Burnside Groups”, Geom. Topol., 21:4 (2017), 1969–2014  crossref  isi
    63. Nekrashevych V., “Palindromic Subshifts and Simple Periodic Groups of Intermediate Growth”, Ann. Math., 187:3 (2018), 667–719  crossref  isi
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