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Mat. Sb., 1991, Volume 182, Number 4, Pages 568–592 (Mi msb1311)  

This article is cited in 101 scientific papers (total in 102 papers)

A solution of the restricted Burnside problem for 2-groups

E. I. Zel'manov

Abstract: A solution is given of the restricted Burnside problem for 2-groups.

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English version:
Mathematics of the USSR-Sbornik, 1992, 72:2, 543–565

Bibliographic databases:

UDC: 512.554.322
MSC: Primary 20F05; Secondary 17B30, 17C10
Received: 19.06.1990

Citation: E. I. Zel'manov, “A solution of the restricted Burnside problem for 2-groups”, Mat. Sb., 182:4 (1991), 568–592; Math. USSR-Sb., 72:2 (1992), 543–565

Citation in format AMSBIB
\by E.~I.~Zel'manov
\paper A~solution of the restricted Burnside problem for 2-groups
\jour Mat. Sb.
\yr 1991
\vol 182
\issue 4
\pages 568--592
\jour Math. USSR-Sb.
\yr 1992
\vol 72
\issue 2
\pages 543--565

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    1. E. I. Khukhro, “Local nilpotency in varieties of groups with operators”, Russian Acad. Sci. Sb. Math., 78:2 (1994), 379–396  mathnet  crossref  mathscinet  zmath  isi
    2. Vaughanlee M. Zelmanov E., “Upper-Bounds in the Restricted Burnside Problem”, J. Algebra, 162:1 (1993), 107–145  crossref  mathscinet  isi
    3. Traustason G., “Engel Lie-Algebras”, Q. J. Math., 44:175 (1993), 355–384  crossref  mathscinet  zmath  isi
    4. Endimioni G., “Finiteness Conditions for a Group of Finite Exponent”, J. Algebra, 155:2 (1993), 290–297  crossref  mathscinet  zmath  isi
    5. Vaughanlee M., “The Nilpotency Class of Finite-Groups of Exponent-P”, Trans. Am. Math. Soc., 346:2 (1994), 617–640  crossref  mathscinet  isi
    6. Martinez C., “On Power Subgroups of Profinite Groups”, Trans. Am. Math. Soc., 345:2 (1994), 865–869  crossref  mathscinet  zmath  isi
    7. Lennox J., Longobardi P., Maj M., Smith H., Wiegold J., “Some Finiteness Conditions Concerning Intersections of Conjugates of Subgroups”, Glasg. Math. J., 37:3 (1995), 327–335  crossref  mathscinet  zmath  isi
    8. Traustason G., “On 4-Engel Groups”, J. Algebra, 178:2 (1995), 414–429  crossref  mathscinet  zmath  isi
    9. Traustason G., “A Polynomial Upper Bound for the Nilpotency Classes of Engel-3 Lie-Algebras Over a Field of Characteristic .2.”, J. Lond. Math. Soc.-Second Ser., 51:Part 3 (1995), 453–460  crossref  mathscinet  zmath  isi
    10. Smith H., “Groups with Finitely Many Conjugacy Classes of Subgroups with Large Subnormal Defect”, Glasg. Math. J., 37:Part 1 (1995), 69–71  crossref  mathscinet  zmath  adsnasa  isi
    11. Martinez C., “Power Subgroups of Pro-(Finite Soluble) Groups”, Bull. London Math. Soc., 28:Part 5 (1996), 481–487  crossref  mathscinet  zmath  isi
    12. Mann A., Martinez C., “The Exponent of Finite Groups”, Arch. Math., 67:1 (1996), 8–10  crossref  mathscinet  zmath  isi
    13. Smith H., Wiegold J., “Locally Graded Groups with All Subgroups Normal-by-Finite”, J. Aust. Math. Soc. A-Pure Math. Stat., 60:2 (1996), 222–227  crossref  mathscinet  zmath  isi
    14. Point F., “Milnor Identities”, Commun. Algebr., 24:12 (1996), 3725–3744  crossref  mathscinet  zmath  isi
    15. David M. Riley, James F. Semple, “Power closure and the Engel condition”, Isr J Math, 97:1 (1997), 281  crossref  mathscinet  zmath  isi
    16. Casacuberta C., Rodriguez J., “On Towers Approximating Homological Localizations”, J. Lond. Math. Soc.-Second Ser., 56:Part 3 (1997), 645–656  crossref  mathscinet  zmath  isi
    17. Burns R., Macedonska O., Medvedev Y., “Groups Satisfying Semigroup Laws, and Nilpotent-by-Burnside Varieties”, J. Algebra, 195:2 (1997), 510–525  crossref  mathscinet  zmath  isi
    18. Endimioni G., “On the Locally Finite P-Groups in Certain Varieties of Groups”, Q. J. Math., 48:190 (1997), 169–178  crossref  mathscinet  zmath  isi
    19. VaughanLee M., “Engel-4 Groups of Exponent 5”, Proc. London Math. Soc., 74:Part 2 (1997), 306–334  crossref  mathscinet  isi
    20. S. P. Strunkov, K.-P. Shum, “On a Burnside-type problem for finite semigroups”, Russian Math. Surveys, 53:1 (1998), 223–224  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    21. Mann A., Martinez C., “Groups Nearly of Prime Exponent and Nearly Engel Lie Algebras”, Arch. Math., 71:1 (1998), 5–11  crossref  mathscinet  zmath  isi
    22. Traustason G., “A Constructive Approach to Zel'Manov's Global Nilpotency Theorem for N-Engel Lie Algebras Over a Field of Characteristic Zero”, Int. J. Algebr. Comput., 8:3 (1998), 317–326  crossref  mathscinet  zmath  isi
    23. Amberg B., Dickenschied O., Sysak Y., “Subgroups of the Adjoint Group of a Radical Ring”, Can. J. Math.-J. Can. Math., 50:1 (1998), 3–15  crossref  mathscinet  zmath  isi
    24. Vaughan-Lee M., “On Zel'Manov's Solution of the Restricted Burnside Problem”, J. Group Theory, 1:1 (1998), 65–94  crossref  mathscinet  zmath  isi
    25. Bovdi A., “The Group of Units of a Group Algebra of Characteristic P”, Publ. Math.-Debr., 52:1-2 (1998), 193–244  mathscinet  zmath  isi
    26. 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
    27. Shumyatsky P., “On Groups with Commutators of Bounded Order”, Proc. Amer. Math. Soc., 127:9 (1999), 2583–2586  crossref  mathscinet  zmath  isi
    28. Groves D., “A Note on Nonidentical Lie Relators”, J. Algebra, 211:1 (1999), 15–25  crossref  mathscinet  zmath  isi
    29. Endimioni G., “On Conditions for a Group to Satisfy Given Laws”, J. Group Theory, 2:2 (1999), 191–198  crossref  mathscinet  zmath  isi
    30. S.P. Strunkov, K.P. Shum, “A Theorem in Semigroups Inspired by the Restricted Burnside Problem”, Journal of Algebra, 226:1 (2000), 621  crossref  mathscinet  zmath
    31. Delizia C., Rhemtulla A., Smith H., “Locally Graded Groups with a Nilpotency Condition on Infinite Subsets”, J. Aust. Math. Soc. A-Pure Math. Stat., 69:Part 3 (2000), 415–420  crossref  mathscinet  zmath  isi
    32. Shumyatsky P., “Verbal Subgroups in Residually Finite Groups”, Q. J. Math., 51:4 (2000), 523–528  crossref  mathscinet  zmath  isi
    33. Segal D., “Closed Subgroups of Profinite Groups”, Proc. London Math. Soc., 81:Part 1 (2000), 29–54  crossref  mathscinet  zmath  isi
    34. Macedonska O., “Collapsing Groups and Positive Laws”, Commun. Algebr., 28:8 (2000), 3661–3666  crossref  mathscinet  zmath  isi
    35. Shumyatsky P., “Applications of Lie Ring Methods to Group Theory”, Nonassociative Algebra and its Applications, Lecture Notes in Pure and Applied Mathematics, 211, ed. Costa R. Grishkov A. Guzzo H. Peresi L., Marcel Dekker, 2000, 373–395  mathscinet  zmath  isi
    36. Tullio Ceccherini-silberstein, Antonio Machì, Fabio Scarabotti, “Il gruppo di Grigorchuk di crescita intermedia”, Rend Circ Mat Palermo, 50:1 (2001), 67  crossref  mathscinet  zmath
    37. David M. Riley, “ALGEBRAS WITH COLLAPSING MONOMIALS. II”, Communications in Algebra, 29:7 (2001), 2745  crossref  mathscinet  zmath  elib
    38. Longobardi P., “On Locally Graded Groups with an Engel Condition on Infinite Subsets”, Arch. Math., 76:2 (2001), 88–90  crossref  mathscinet  zmath  isi
    39. Shumyatsky P., “On Profinite Groups in Which Commutators Are Engel”, J. Aust. Math. Soc. A-Pure Math. Stat., 70:1 (2001), 1–9  crossref  mathscinet  zmath  isi
    40. Freese R., Jezek J., Nation J., “Lattices with Large Minimal Extensions”, Algebr. Universalis, 45:2-3 (2001), 221–309  crossref  mathscinet  isi
    41. Abdollahi A. Traustason G., “On Locally Finite P-Groups Satisfying an Engel Condition”, Proc. Amer. Math. Soc., 130:10 (2002), 2827–2836  crossref  mathscinet  zmath  isi
    42. Endimioni G., “Bounds for Nilpotent-by-Finite Groups in Certain Varieties”, J. Aust. Math. Soc., 73:3 (2002), 393–404  crossref  mathscinet  zmath  isi
    43. Shumyatsky P., “Commutators in Residually Finite Groups”, Mon.heft. Math., 137:2 (2002), 157–165  crossref  mathscinet  zmath  isi
    44. Kuzucouoglu M., Shumyatsky P., “On Local Finiteness of Periodic Residually Finite Groups”, Proc. Edinb. Math. Soc., 45:3 (2002), 717–721  crossref  mathscinet  isi
    45. Shumyatsky P., “On Varieties Arising From the Solution of the Restricted Burnside Problem”, J. Pure Appl. Algebr., 171:1 (2002), 67–74  crossref  mathscinet  zmath  isi
    46. Shumyatsky P., “A (Locally Nilpotent)-by-Nilpotent Variety of Groups”, Math. Proc. Camb. Philos. Soc., 132:2 (2002), 193–196  crossref  mathscinet  zmath  isi
    47. Corson J., Ratkovich T., “On Profinite Groups Whose Power Subgroups Are Closed”, Commun. Algebr., 30:9 (2002), 4189–4196  crossref  mathscinet  zmath  isi
    48. Crvenkovic S., Tasic V., “Decidability of Semigroup Identities in Soluble Groups”, J. Group Theory, 5:1 (2002), 107–118  mathscinet  zmath  isi
    49. Burns R., Medvedev Y., “Group Laws Implying Virtual Nilpotence”, J. Aust. Math. Soc., 74:3 (2003), 295–312  crossref  mathscinet  zmath  isi
    50. Groves D., Vaughan-Lee M., “Finite Groups of Bounded Exponent”, Bull. London Math. Soc., 35:Part 1 (2003), 37–40  crossref  mathscinet  zmath  isi
    51. Medvedev Y., “On Compact Engel Groups”, Isr. J. Math., 135 (2003), 147–156  crossref  mathscinet  zmath  isi
    52. De Falco M., de Giovanni F., Musella C., “Groups in Which Every Subgroup Is Permutable-by-Finite”, Commun. Algebr., 32:3 (2004), 1007–1017  crossref  mathscinet  zmath  isi
    53. S. V. Ivanov, A. M. Storozhev, “Non-Hopfian Relatively Free Groups”, Geom Dedicata, 114:1 (2005), 209  crossref  mathscinet  zmath  isi
    54. Traustason G., “Milnor Groups and (Virtual) Nilpotence”, J. Group Theory, 8:2 (2005), 203–221  crossref  mathscinet  zmath  isi  elib
    55. Moravec P., “Some Groups with N-Central Normal Closures”, Publ. Math.-Debr., 67:3-4 (2005), 355–372  mathscinet  zmath  isi
    56. Endimioni G., Traustason G., “On Varieties in Which Soluble Groups Are Torsion-by-Nilpotent”, Int. J. Algebr. Comput., 15:3 (2005), 537–545  crossref  mathscinet  zmath  isi
    57. Shumyatsky P., “Elements of Prime Power Order in Residually Finite Groups”, Int. J. Algebr. Comput., 15:3 (2005), 571–576  crossref  mathscinet  zmath  isi  elib
    58. Riley D., Shumyatsky P., “Groups with a Positive Law on Commutators”, J. Pure Appl. Algebr., 195:3 (2005), 293–299  crossref  mathscinet  zmath  isi  elib
    59. Shumyatsky P., “A Variety of Groups”, Math. Proc. Camb. Philos. Soc., 138:1 (2005), 21–26  crossref  mathscinet  zmath  isi  elib
    60. Daniel Goldstein, Robert M Guralnick, “The direct product theorem for profinite groups”, jgth, 9:3 (2006), 317  crossref  mathscinet  zmath  isi
    61. Costantino Delizia, Mohammad Reza R Moghaddam, Akbar Rhemtulla, “The structure of Bell groups”, jgth, 9:1 (2006), 117  crossref  mathscinet  zmath  isi
    62. Moravec P., “On Power Endomorphisms of N-Central Groups”, J. Group Theory, 9:4 (2006), 519–536  crossref  mathscinet  zmath  isi
    63. Efim Zelmanov, “SOME OPEN PROBLEMS IN THE THEORY OF INFINITE DIMENSIONAL ALGEBRAS”, Journal of the Korean Mathematical Society, 44:5 (2007), 1185  crossref  mathscinet  zmath  isi  elib
    64. Sapir, MV, “Some group theory problems”, International Journal of Algebra and Computation, 17:5–6 (2007), 1189  crossref  mathscinet  zmath  isi  elib
    65. Kuzucuoglu M., “Barely Transitive Groups”, Turk. J. Math., 31:S (2007), 79–94  mathscinet  zmath  isi
    66. Shumyatsky P., “Engel Values in Residually Finite Groups”, Mon.heft. Math., 152:2 (2007), 169–175  crossref  mathscinet  zmath  isi
    67. Delizia C., Moravec P., Nicotera Ch., “Locally Graded Bell Groups”, Publ. Math.-Debr., 71:1-2 (2007), 1–9  mathscinet  zmath  isi
    68. Nikolov N., Segal D., “On Finitely Generated Profinite Groups, I: Strong Completeness and Uniform Bounds”, Ann. Math., 165:1 (2007), 171–238  crossref  mathscinet  zmath  isi
    69. Plaumann P., Sabinina L., “On Nuclearly Nilpotent Loops of Finite Exponent”, Commun. Algebr., 36:4 (2008), 1346–1353  crossref  mathscinet  zmath  isi
    70. D. Osin, “On the Universal Theory of Torsion and Lacunary Hyperbolic Groups”, Groups – Complexity – Cryptology, 1:2 (2009), 311  crossref  mathscinet  zmath
    71. Shumyatsky P., Silva J.C., “Varieties of groups and the restricted Burnside problem”, Ischia: Group Theory 2008, 2009, 248–257  crossref  mathscinet  zmath  isi
    72. Shumyatsky P., Silva J.C., “The Restricted Burnside Problem for Multilinear Commutators”, Math. Proc. Camb. Philos. Soc., 146 (2009), 603–613  crossref  mathscinet  zmath  isi
    73. Brandl R., “Groups with Commuting Powers”, Bull. Aust. Math. Soc., 79:2 (2009), 343–351  crossref  mathscinet  zmath  isi
    74. A. A. Kuznetsov, K. A. Filippov, “Ob odnom involyutivnom avtomorfizme Bernsaidovoi gruppy $B_0(2,5)$”, Sib. zhurn. industr. matem., 13:3 (2010), 68–75  mathnet  mathscinet
    75. 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
    76. A. A. Kuznetsov, K. A. Filippov, “Ob odnom avtomorfizme poryadka 2 bernsaidovoi gruppy $B_0(2,5)$”, Vladikavk. matem. zhurn., 12:4 (2010), 44–48  mathnet  elib
    77. Crosby P.G. Traustason G., “On Right N-Engel Subgroups”, J. Algebra, 324:4 (2010), 875–883  crossref  mathscinet  zmath  isi
    78. Vaughan-Lee M., “An Insoluble (P-2)-Engel Group of Exponent P”, J. Algebra, 323:6 (2010), 1826–1838  crossref  mathscinet  zmath  isi
    79. Shumyatsky P., Silva J.C., “Engel Words and the Restricted Burnside Problem”, Mon.heft. Math., 159:4 (2010), 397–405  crossref  mathscinet  zmath  isi
    80. Shumyatsky P., “Positive Laws in Fixed Points of Automorphisms of Finite Groups”, J. Pure Appl. Algebr., 215:11 (2011), 2559–2566  crossref  mathscinet  zmath  isi  elib
    81. Caldeira J., Shumyatsky P., “On Verbal Subgroups in Residually Finite Groups”, Bull. Aust. Math. Soc., 84:1 (2011), 159–170  crossref  mathscinet  zmath  isi  elib
    82. Shumyatsky P., “On the Exponent of a Finite Group with an Automorphism Group of Order Twelve”, J. Algebra, 331:1 (2011), 482–489  crossref  mathscinet  zmath  isi  elib
    83. Shumyatsky P., “Commutators in Residually Finite Groups”, Isr. J. Math., 182:1 (2011), 149–156  crossref  mathscinet  zmath  isi  elib
    84. K. A. Filippov, “O tsentralizatorakh avtomorfizmov bernsaidovoi gruppy $B_0(2,5)$”, Sib. elektron. matem. izv., 9 (2012), 185–189  mathnet
    85. V. D. Mazurov, W. J. Shi, “A criterion of unrecognizability by spectrum for finite groups”, Algebra and Logic, 51:2 (2012), 160–162  mathnet  crossref  mathscinet  zmath  isi
    87. Filippov K.A., “O diametre keli odnoi podgruppy gruppy v _{0} (2,5)”, Vestnik sibirskogo gosudarstvennogo aerokosmicheskogo universiteta im. akademika M.F. Reshetneva, 2012, no. 1, 234–236  elib
    88. Shumyatsky P., “Exponent of a Finite Group with a Four-Group of Automorphisms”, Mon.heft. Math., 168:1 (2012), 113–124  crossref  mathscinet  zmath  isi
    89. Akhavi A., Klimann I., Lombardy S., Mairesse J., Picantin M., “On the Finiteness Problem for Automaton (Semi) Groups”, Int. J. Algebr. Comput., 22:6 (2012), 1250052  crossref  mathscinet  zmath  isi
    90. N. V. Maslova, D. O. Revin, “Finite groups whose maximal subgroups have the Hall property”, Siberian Adv. Math., 23:3 (2013), 196–209  mathnet  crossref  mathscinet  elib
    91. Shumyatsky P., “On the Exponent of a Verbal Subgroup in a Finite Group”, J. Aust. Math. Soc., 93:3 (2012), 325–332  crossref  mathscinet  zmath  isi
    92. Shumyatsky P., “Exponent of a Finite Group with a Fixed-Point-Free Four-Group of Automorphisms”, Isr. J. Math., 194:2 (2013), 895–906  crossref  mathscinet  zmath  isi
    93. Kurdachenko L.A., Shumyatsky P., “The Ranks of Central Factor and Commutator Groups”, Math. Proc. Camb. Philos. Soc., 154:1 (2013), 63–69  crossref  mathscinet  zmath  isi
    94. Evgeny I. Khukhro, “Problems of bounding the $p$-length and Fitting height of finite soluble groups”, Zhurn. SFU. Ser. Matem. i fiz., 6:4 (2013), 462–478  mathnet
    95. Lima E., Shumyatsky P., “On Locally Finite Groups with a Four-Subgroup Whose Centralizer Is Small”, Mon.heft. Math., 172:1 (2013), 77–84  crossref  mathscinet  zmath  isi
    96. Lima E.N., Shumyatsky P., “On the Structure of Locally Finite Groups with Small Centralizers”, J. Algebra, 398 (2014), 303–309  crossref  mathscinet  zmath  isi
    97. Brendan Murphy, Jonathan Pakianathan, “Kakeya configurations in Lie groups and homogeneous spaces”, Topology and its Applications, 180 (2015), 1  crossref  mathscinet  zmath
    98. O. B. Finogenova, “Pochti lievo nilpotentnye nepervichnye mnogoobraziya assotsiativnykh algebr”, Tr. IMM UrO RAN, 21, no. 4, 2015, 282–291  mathnet  mathscinet  elib
    99. Proc. Steklov Inst. Math., 292 (2016), 216–246  mathnet  crossref  crossref  mathscinet  isi  elib
    100. L. A. Bokut', E. S. Golod, R. I. Grigorchuk, V. N. Zhelyabin, V. G. Kats, A. R. Kemer, V. V. Kirichenko, P. S. Kolesnikov, S. S. Kutateladze, V. N. Latyshev, Yu. N. Maltsev, G. A. Margulis, A. V. Mikhalev, A. G. Myasnikov, S. P. Novikov, A. Yu. Ol'shanskii, A. N. Parshin, V. P. Platonov, Yu. G. Reshetnyak, N. S. Romanovskii, I. A. Taimanov, O. G. Kharlampovich, V. K. Kharchenko, L. N. Shevrin, I. P. Shestakov, A. V. Yakovlev, “Efim Isaakovich Zelmanov is 60 years old”, Russian Math. Surveys, 71:4 (2016), 793–800  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    101. L. A. Bokut, “Early history of the theory of rings in Novosibirsk”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 2, 5–23  mathnet  mathscinet
    102. S. O. Gorchinskiy, Vik. S. Kulikov, A. N. Parshin, V. L. Popov, “Igor Rostislavovich Shafarevich and His Mathematical Heritage”, Proc. Steklov Inst. Math., 307 (2019), 1–21  mathnet  crossref  crossref  isi  elib
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