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Alexander Olshanskiy

Publications

  1. On the residual property of groups, Vestnik Mosk. Univ., Ser. Matem. (1968), N 2, 60–62, Russian (with K. K. Andreyev).
  2. On a Hanna Neumann’s problem, Matem. Sbornik (1968), N 3, 449–453 (in Russian).
  3. Varieties of residually finite groups, Izvestia Akad. Nauk SSSR, Ser. Matem. (1969), N 4, 915–927 (in Russian).
  4. On the problem of a finite basis of identities for groups, Izvestia Akad. Nauk SSSR, Ser. Matem.(1970), N 2, 376–384 (in Russian).
  5. Two remarks on varieties of groups, Vestnik Mosk. Univ., Ser. Matem. (1971) N 2, 45–50 (in Russian).
  6. Some questions of the theory of group varieties, Ph. D. thesis, Mosc. Univ., Dept. of Mechanics and Mathematics, 1971 (in Russian).
  7. Solvable just-non-Cross varieties of groups, Matem. Sbornik (1971), N 5, 115–131 (in Russian).
  8. On orders of relatively free groups of locally finite varieties, Izvestia Akad. Nauk SSSR, Ser. Matem. (1973), N1, 89–94 (in Russian).
  9. On characteristic subgroups of free groups, Uspekhi Matem. Nauk (1974), N 1, 179–180 (in Russian).
  10. Quasiidentities in finite groups, Sibirsk. Matem. J. (1974), 1409–1413 (in Russian).
  11. Identical relations in finite Lie rings, Matem. Sbornik (1975), N 4, 543–559, in Russian (joint with Yu. A. Bakhturin).
  12. On residual property and characteristic subalgebras of free Lie algebras, Trudy Sem. im. I.G.Petrovskogo (1976), N 2, 145–150, in Russian (with Yu. A. Bakhturin).
  13. Solvable just-non-Cross varieties of Lie rings, Matem. Sbornik (1976), N 3, 384–399, in Russian (joint with Yu. A. Bakhturin).
  14. To the questions on the number of generators and orders of abelian subgroups of finite p-groups, Matem. Zametki (1978), N3, 345–350 (in Russian).
  15. On some infinite sets of identities, Trudy Sem. im. I. G. Petrovskogo (1978), N 3, 139–145 (in Russian).
  16. Investigation of locally finite varieties of groups, Doctor of Sci. Thesis (1979), Moscow State Univ., Dept. of Mechanics and Mathematics (in Russian).
  17. Infinite groups with cyclic subgroups, Doklady Akad. Nauk SSSR, 245 (1979), N 4, 785–787 (in Russian).
  18. An infinite simple Noetherian torsion free group, Izvestia Akad. Nauk SSSR, Ser. Matem. (1979), N 6, 1328–1393 (in Russian).
  19. On groups with cyclic subgroups, Doklady Bulg. Akad. Nauk 32 (1979), N 5, 1165–1166 (in Russian).
  20. An infinite group with subgroups of prime orders, Izvestia Akad. Nauk SSSR, Ser. Matem., 44 (1980), N 2, 309–321 (in Russian).
  21. To the question on the existence of an invariant mean on a group, Uspekhi Matem. Nauk (1980), N 4, 199–200 (in Russian).
  22. Remark on a countable non-topologizable group, Vestnik Mosk. Univ., Ser. Matem. (1980), N 3, 103 (in Russian).
  23. On Novikov – Adian’s theorem, Matem. Sbornik, 118 (1982),n 2,203–235 (in Russian).
  24. Groups of a finite exponent with subgroups of a prime order, Algebra and Logika (1982), N 5, 553–618 (in Russian).
  25. Practical work in algebra, Moscow State Univ. Publ (1983) 92 pages, in Russian (jointly with a team of authors).
  26. Collection of exercises in algebra, Parts 1,2,3,4, Moscow State Univ. Publ. (1983, 1984, 1985, 1986), 148+184+104+72 pages, in Russian (jointly with a team of authors).
  27. On a geometric method in combinatorial group theory, Proc. Int. Congress Math. 1(1983), 415–424.
  28. On abelian and central extensions of aspherical groups, Izvestia Vuzov, Matem. (1985), N 11, 48–60, in Russian (with I. S. Ashmanov).
  29. Varieties in which all finite groups are abelian, Matem. Sbornik, 126 (1985), N 1, 59–82 (in Russian).
  30. Subgroups of quasifinite groups, Uspekhi Matem. Nauk, 41 (1986), N 6, 169–170, in Russian (joint with G. S. Deryabina).
  31. The Neumanns – Shmel’kin’s theorem, Vestnik Mosk. Univ., Ser. Matem.(1986), N 6, 61–64 (in Russian).
  32. Collection of exercises in algebra, Moscow, Nauka (1987, 1995, 2001, 2006), 352 pages, in Russian (in a team of authors).
  33. Identical relations, Sovremen. problemy matem. Fundament. napravl., 117–240: in Itogi Nauki i Tekhniki VINITI AN SSSR, 18, Moscow, 1988,
    in Russian (with Yu. A. Bakhturin).
  34. The Mal’tsev problem on operations on groups, Trudy Sem. im. I. G. Petrovskogo, 14 (1989), 225–249 (in Russian)
  35. Geometry of defining relations in groups, Moscow, Nauka, 1989, 448 pages (in Russian, English translation by Kluwer Academic Publ., 1991).
  36. Thrifty embeddings of countable groups, Vestnik Mosk. Univ., Ser. Matem. (1989), N 2, 28–34 (in Russian).
  37. Infinite groups, Sovremen. problemy matem., Fundament. napravl., 5–113; in Itogi Nauki i Tekhniki VINITI AN SSSR, 37, Moscow, 1989, in Russian (with A. L. Shmel’kin).
  38. Diagrams of homomorphisms of surface groups, Sibirsk. Matem. J., 30 (1989), N 6, 150–171 (in Russian).
  39. Some applications of graded diagrams in combinatorial group theory, London Math. Soc., Lecture Notes Ser., 160 (1990), 258–308 (with S. V. Ivanov).
  40. Embedding of countable periodic groups into 2-generator simple periodic groups, Ukrain. Matem. J., 43 (1991), N 7-8, 980–986 (in Russian).
  41. Hyperbolicity of groups with subquadratic isoperimetric inequality, Intern. J. of Algebra and Computation 1 (1991), N 3, 281–289 .
  42. Periodic quotients of hyperbolic groups, Matem. Sbornik., 182 (1991), N 4, 543–567 (in Russian).
  43.  Almost every group is hyperbolic, Internat J. of Algebra and Comput., 2 (1992), N 1, 1–17.
  44. On two problems of H. Neumann about linked products of groups, Bull. Austral. Math. Soc., 46 (1992), 2, 311–315 (joint with S. V. Ivanov).
  45. Embedding of periodic groups into simple periodic groups, Ukrain. Matem. J., 44 (1992), N 6, 845–847 (in Russian).
  46. On residualing homomorphisms and G-subgroups of hyperbolic groups, Internat. J. of Algebra and Comput., 3 (1993), 1–44.
  47. On calculation of width in free groups, London Math. Soc., Lecture Notes Ser., 204 (1995), 255–258.
  48. A simplification of Golod’s example, Proc. 3rd Int. Conf. in Group Theory (Korea, Pusan, 1994), Walter de Gryuter (1995), 263–265.
  49. SQ-universality of hyperbolic groups, Matem. Sbornik, 186 (1995), N 8, 119–132 (in Russian).
  50. A group variety defined by a semigroup law, J. Austral. Math. Soc. (Series A) 60 (1996), 255–259 (with A.Storozhev).
  51. Genericity of the class of groups in which subgroups with fewer number of generators are free, Matem. Zametki, 59 (1996), N 4, 489–496 (in Russian; with G. N. Arzhantseva).
  52. Hyperbolic groups and their quotients of finite exponent, Trans. Amer. Math. Soc. 348 (1996) N 6, 2091–2138 (with S. V. Ivanov).
  53. On finite and locally finite subgroups of free Burnside groups of large even exponents, Journal of Algebra, 195(1997), 241–284 (with S. V. Ivanov).
  54. On the subgroup distortion in finitely presented groups, Matem. Sbornik, 188 (1997), N 11, 73–120 (in Russian).
  55. Some constructions relating to hyperbolic groups, London Math. Soc. Lecture Notes Ser., 252 (1998), 263–290 (joint with K. V. Mikhajlovskii).
  56. Distortion functions for subgroups, in “Geometric Group Theory Down Under”, Proc. of a Special Year in Geometric Group Theory, Canberra, Australia, 1996, Ed. J.Cossey,…, Walter de Gruyter, Berlin – New York, 1999, 281–291.
  57. The growth of finite subgroups in p-groups, London Math. Soc. Lect. Note Ser. 261 (1999), 579–595.
  58. Quadratic isoperimetric functions of the Heisenberg groups. A combinatorial proof, Algebra, 11, J. Math. Sci. (new York) 93 (1999), no. 6,, 921–927 (with M. V. Sapir).
  59. Length functions on subgroups in finitely presented groups, In ” Groups – Korea ‘ 98 “, Proc. Intern. Conf., Pusan, Korea, 1998, Ed. Young Gheel Baik …, Walter de Gruyter, Berlin — New York, 2000, 297–304 (with M.V.Sapir).
  60. Embeddings of relatively free groups into finitely presented groups, Contemp.Math., 264 (2000), 23–47 (joint with M.V.Sapir)
  61. On the Bass – Lubotzky question about quotients of hyperbolic groups, Journal of Algebra, 226 (2000), 807–817 .
  62. Length and area functions in groups and quasi-isometric Higman embeddings, Intern. J. Algebra and Comput., 11 (2001), no. 2 , 137–170 (with M.V.Sapir).
  63. Non-amenable finitely presented torsion-by-cyclic groups, Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 45–53 (http://www.ams.org/era ; with M.V.Sapir).
  64. Comparison of products of the varieties of Lie algebras, Communications in Algebra, 29(2001), no. 9, 4267–4275 (with. A.L. Shmelkin).
  65. Isoperimetric functions of groups and combinatorial complexity of the word problem , Annals of Mathematics , 156 (2002), no. 2, 467–518 (with J.-C. Birget, E.Rips, M.Sapir).
  66. Non-amenable finitely presented torsion-by-cyclic groups, Publ. Math. IHES, 96 (2003), no. 6, p.p. 43–169 (with M.V.Sapir).
  67. Self-normalization of free subgroups in the free Burnside groups,in “Groups, Rings and Lie Algebras”, Kluwer AP, 2003, 179–187.
  68. Conjugacy problem for groups and Higman embeddings, Electronic Res. Announc. of the AMS”, 9 (2003), 40–50 (with M.V.Sapir).
  69. Conjugacy problem and Higman embeddings, “Memoirs of the AMS” 170(2004), no. 804 p.p. vii+131 (with M.V.Sapir)
  70. Subgroups of finitely presented groups with solvable conjugacy problem, Intern. J. Algebra and Comput., 15, no. 5-6 (2005), 1–10 (with M.V.Sapir)
  71. Groups with non-simply connected asymptotic cones, “Contemporary Mathematics”, 394 (2006),203–208 (with M.V.Sapir).
  72. Groups with small Dehn functions and bipartite chord diagrams, “Geometric and Functional Analysis”, 16 (2006), 1324–1376 (with M.V.Sapir).
  73. On finite definability of groups F/[M,N], “Vestnik Moskovskogo Universiteta” (Proc. of the Moscow State University), Ser. 1, 2007, no.6, 19–21 (with O.V.Kulikova, also see arXiv.math)
  74. Groups with quadratic-non-quadratic Dehn functions, “Intern. J. Algebra and Comput.”, 17(2007), no. 2, p.p. 401–419.
  75. A finitely presented group with two non-homeomorphic asymptotic cones, “Intern. J. Algebra and Comput.”, 17(2007), no.2, p.p. 421–426 (with M.V.Sapir)
  76. Large restricted Lie algebras, “Journal of Algebra”, 310 (2007), no. 1, 413–427 (with Yu.A.Bahturin).
  77. Linear automorphism groups of relatively free groups. “Turkish Journal of Mathematics”, 31(2007) (suppl., dedicated to the memory of Brian Hartley), 105–111.
  78. A 2-generated 2-related group with no non-trivial finite quotients. “Algebra and Discrete Math.” 2007, no. 2, 111–114 (with M.V.Sapir).
  79. Large groups and their periodic quotients. “Proc. of the AMS”, 136 (2008), no. 3, 753–759 (with D.V.Osin).
  80. On products of T-ideals in free algebras and free group algebras. “Journal of Pure and Applied Algebra”, 213(2009), no. 2, 259–263.
  81. Schreier rewriting beyond the classical setting. “Science in China”, Ser. A, Mathematics (Springer), 52 (2009), no.2, 231–243 (with Yu.A.Bahturin).
  82. Lacunarly hyperbolic groups. “Geometry and Topology”, 13(2009), no. 4, 2051–2140 (with D.V.Osin and M.V.Sapir).
  83. Periodic quotients of hyperbolic and large groups. “Groups, Geometry and Dynamics”, 3(2009), no.3, 423–452 (with A.Minasyan and D.Sonkin).
  84. On Fk-like groups. “Algebra and Logic”, 48(2009), no.2, 140–146 (with M.V.Sapir).
  85. Actions of maximal growth, “Proceedings of the London Math. Soc.” 101 (2010), no.1, 27–72 (with Yu.A.Bahturin).
  86. Filtrations and distortion in infinite-dimensional algebras, “Journal of Algebra”, 327 (2011), 251–291 (with Yu.A.Bahturin).
  87. Subgroup distortion in wreath products of cyclic groups, “Journal of Pure and Applied Algebra”, 215(2011) 2987–3004 (with Tara Davis).
  88. Space functions of groups, “Trans. Amer. Math. Soc”, 364 (2012), 4937–4985.
  89. Groups with undecidable word problem and almost quadratic Dehn function, “Journal of Topology” 5 (2012), no.4, 785–886 (with Appendix written by M.V.Sapir).
  90. A quasi-isometric embedding theorem for groups,“Duke Math. Journal”, 162 (2013), no.9, 1621–1648 (with D.V.Osin).
  91. Space functions and space complexity of the word problem in semigroups, “Computational Complexity”, 22 (2013), no.4, pp. 771–830.
  92. On topologizable and non-topologizable groups, “Topology and its Applications”, 160 (2013), 2104-2120 (with Ant.A. Klyachko and D.V.Osin).
  93. On abelian subgroups of finitely generated metabelian groups,
    “Journal of Group Theory”, 16 (2013), no.5, 695–705 (with V.H.Mikaelian).
  94. C*-simple groups without free subgroups, “Groups, Geometry and Dynamics”, 8 (2014), 933-983. (with D.V.Osin).
  95. Growth of subalgebras and subideals in free Lie algebras, “Journal of Algebra” 422 (2015), 277-305 (with Yu.A.Bahturin).
  96. Relative subgroup growth and subgroup distortion, “Groups, Geometry and Dynamics”, 9 (2015), no.1, 237-273 (with Tara Davis).
  97. On infinite groups of finite exponent, “Algebra and Logica”, 54 (2015), no. 2, 243-251, in Russian, English translation in Algebra and Logic: Volume 54, Issue 2 (2015) (with V.D. Mazurov and A.I.Sozutov).
  98. On identities in the products of group varieties, “Intern. J. of Algebra and Comput.”, v. 25 (2015), no. 3, 531-540 (with N.S. Boatman).
  99. On pairs of finitely generated subgroups in free groups, “Proceedings AMS”, 143 (2015), 4177-4188.
  100. Diagonal bi-acts over semigroups with finiteness conditions, “Semigroup Forum”, 91 (2015), no. 2, 538-542 (with I.B. Kozhukhov).
  101. Constructions of torsion-free countable, amenable, weakly mixing groups, L’Enseignement Mathematique” (2), 61 (2015), 321-342; (with R. Grigorchuk and R. Kravchenko).
  102. On Kaluzhnin – Krasner’s embeddings of groups, Algebra Discrete Math. 19 (2015), no. 1, 77-86.
  103. Embedding construction based on amalgamations of group relators, “Journal of Topology and Analysis”, 8 (2016), no. 1, 1-24.
  104. Subnormal subgroups in free groups, their growth and co-growth, ”Math. Proc. Cambridge Phil. Soc.”, 163 (2017), no. 3, 499-531.
  105. On flat submaps of maps of non-positive curvature, Accepted to ”Transactions of the American Mathematical Society”.
    arXiv:1702.08205, 2017 (with M. Sapir).
  106. On cardinality of sets of relators for the group F/∏[Ni,Nj], “Fundamental and Applied Mathematics”, accepted (with O.V. Kulikova).
  107. Polynomially-bounded Dehn functions of groups, “Journal of Combinatorial Algebra”, 1 – 123, DOI 10.41J1/JCA/2-y-z.
  108. Conjugacy problem in groups with quadratic Dehn function,
    arXiv.math.1809.00280, 83pp. (with M.V. Sapir).