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Izv. RAN. Ser. Mat., 1996, Volume 60, Issue 3, Pages 3–224 (Mi izv77)  

This article is cited in 47 scientific papers (total in 49 papers)

Infinite Burnside groups of even exponent

I. G. Lysenok

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We present a modified version of the Novikov–Adian theory for free Burnside groups of exponent $n=16k\geqslant 8000$. On the basis of this theory, we obtain a negative solution to the Burnside problem for even values of $n\geqslant 8000$ and prove a number of assertions on Burnside groups of exponent $n=16k\geqslant 8000$.


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Izvestiya: Mathematics, 1996, 60:3, 453–654

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Document Type: Article
MSC: Primary 20F50; Secondary 20F05, 20F06
Received: 28.04.1995

Citation: I. G. Lysenok, “Infinite Burnside groups of even exponent”, Izv. RAN. Ser. Mat., 60:3 (1996), 3–224; Izv. Math., 60:3 (1996), 453–654

Citation in format AMSBIB
\by I.~G.~Lysenok
\paper Infinite Burnside groups of even exponent
\jour Izv. RAN. Ser. Mat.
\yr 1996
\vol 60
\issue 3
\pages 3--224
\jour Izv. Math.
\yr 1996
\vol 60
\issue 3
\pages 453--654

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    1. Hammoudi L., “Just-Infinite Nil-Rings and Groups”, Algebr. Colloq., 5:4 (1998), 371–376  mathscinet  zmath  isi
    2. Vaughan-Lee M. Zel'Manov E., “Bounds in the Restricted Burnside Problem”, J. Aust. Math. Soc. A-Pure Math. Stat., 67:Part 2 (1999), 261–271  crossref  mathscinet  zmath  isi
    3. Havas G., Newman M., Niemeyer A., Sims C., “Groups with Exponent Six”, Commun. Algebr., 27:8 (1999), 3619–3638  crossref  mathscinet  zmath  isi  scopus
    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. Ivanov S., “On Finitely Presented Groups Given by Periodic Relators”, J. Group Theory, 3:1 (2000), 95–99  crossref  mathscinet  zmath  isi  scopus  scopus
    6. 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
    7. do Lago A., “Local Groups in Free Groupoids Satisfying Certain Monoid Identities”, Int. J. Algebr. Comput., 12:1-2 (2002), 357–369  crossref  mathscinet  zmath  isi
    8. 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
    9. Hammoudi L., “Burnside and Kurosh Problems”, Int. J. Algebr. Comput., 14:2 (2004), 197–211  crossref  mathscinet  zmath  isi  scopus  scopus
    10. 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
    11. Ivanov S. Storozhev A., “Non-Hopfian Relatively Free Groups”, Geod. Dedic., 114:1 (2005), 209–228  crossref  mathscinet  zmath  isi  scopus  scopus
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    13. I. G. Lysenok, “Burnside structures of finite subgroups”, Izv. Math., 71:5 (2007), 939–965  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. Dani P., “The asymptotic density of finite-order elements in virtually nilpotent groups”, Journal of Algebra, 316:1 (2007), 54–78  crossref  mathscinet  zmath  isi  scopus  scopus
    15. T. Delzant, M. Gromov, “Courbure mesoscopique et theorie de la toute petite simplification”, Journal of Topology, 1:4 (2008), 804  crossref  mathscinet  zmath  isi
    16. Victor Danilovich Mazurov, WuJie Shi, “On periodic groups with prescribed orders of elements”, Sci China Ser A, 52:2 (2009), 311  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    17. V. D. Mazurov, A. S. Mamontov, “On periodic groups with small orders of elements”, Siberian Math. J., 50:2 (2009), 316–321  mathnet  crossref  mathscinet  isi  elib  elib
    18. V. S. Atabekian, “On subgroups of free Burnside groups of odd exponent $n\ge 1003$”, Izv. Math., 73:5 (2009), 861–892  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    19. Minasyan, A, “Periodic quotients of hyperbolic and large groups”, Groups Geometry and Dynamics, 3:3 (2009), 423  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    20. A. Kh. Zhurtov, V. D. Mazurov, “Lokalnaya konechnost nekotorykh grupp s zadannymi poryadkami elementov”, Vladikavk. matem. zhurn., 11:4 (2009), 11–15  mathnet  elib
    21. Grigorchuk R.I. Ivanov S.V., “On Dehn Functions of Infinite Presentations of Groups”, Geom. Funct. Anal., 18:6 (2009), 1841–1874  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    22. 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
    23. 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
    24. V. D. Mazurov, “Periodic groups with prescribed element orders”, Tr. In-ta matem., 18:1 (2010), 72–78  mathnet
    25. Atabekyan V.S., “Non-Phi-Admissible Normal Subgroups of Free Burnside Groups”, J. Contemp. Math. Anal.-Armen. Aca., 45:2 (2010), 112–122  crossref  mathscinet  zmath  isi  scopus  scopus
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    27. Ashot S. Pahlevanyan, “The Fibonacci automorphism of free Burnside groups”, RAIRO-Theor. Inf. Appl, 2011  crossref  mathscinet  isi  scopus  scopus
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    30. Lytkina D.V., “Periodic Groups with Given Properties of Finite Subgroups”, Dokl. Math., 85:1 (2012), 55–56  crossref  mathscinet  zmath  isi  elib  elib  scopus
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