# Publications

- On the residual property of groups, Vestnik Mosk. Univ., Ser. Matem. (1968), N 2, 60–62, Russian (with K. K. Andreyev).
- On a Hanna Neumann’s problem, Matem. Sbornik (1968), N 3, 449–453 (in Russian).
- Varieties of residually finite groups, Izvestia Akad. Nauk SSSR, Ser. Matem. (1969), N 4, 915–927 (in Russian).
- On the problem of a finite basis of identities for groups, Izvestia Akad. Nauk SSSR, Ser. Matem.(1970), N 2, 376–384 (in Russian).
- Two remarks on varieties of groups, Vestnik Mosk. Univ., Ser. Matem. (1971) N 2, 45–50 (in Russian).
- Some questions of the theory of group varieties, Ph. D. thesis, Mosc. Univ., Dept. of Mechanics and Mathematics, 1971 (in Russian).
- Solvable just-non-Cross varieties of groups, Matem. Sbornik (1971), N 5, 115–131 (in Russian).
- On orders of relatively free groups of locally finite varieties, Izvestia Akad. Nauk SSSR, Ser. Matem. (1973), N1, 89–94 (in Russian).
- On characteristic subgroups of free groups, Uspekhi Matem. Nauk (1974), N 1, 179–180 (in Russian).
- Quasiidentities in finite groups, Sibirsk. Matem. J. (1974), 1409–1413 (in Russian).
- Identical relations in finite Lie rings, Matem. Sbornik (1975), N 4, 543–559, in Russian (joint with Yu. A. Bakhturin).
- 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).
- Solvable just-non-Cross varieties of Lie rings, Matem. Sbornik (1976), N 3, 384–399, in Russian (joint with Yu. A. Bakhturin).
- 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).
- On some infinite sets of identities, Trudy Sem. im. I. G. Petrovskogo (1978), N 3, 139–145 (in Russian).
- Investigation of locally finite varieties of groups, Doctor of Sci. Thesis (1979), Moscow State Univ., Dept. of Mechanics and Mathematics (in Russian).
- Infinite groups with cyclic subgroups, Doklady Akad. Nauk SSSR, 245 (1979), N 4, 785–787 (in Russian).
- An infinite simple Noetherian torsion free group, Izvestia Akad. Nauk SSSR, Ser. Matem. (1979), N 6, 1328–1393 (in Russian).
- On groups with cyclic subgroups, Doklady Bulg. Akad. Nauk 32 (1979), N 5, 1165–1166 (in Russian).
- An infinite group with subgroups of prime orders, Izvestia Akad. Nauk SSSR, Ser. Matem., 44 (1980), N 2, 309–321 (in Russian).
- To the question on the existence of an invariant mean on a group, Uspekhi Matem. Nauk (1980), N 4, 199–200 (in Russian).
- Remark on a countable non-topologizable group, Vestnik Mosk. Univ., Ser. Matem. (1980), N 3, 103 (in Russian).
- On Novikov – Adian’s theorem, Matem. Sbornik, 118 (1982),n 2,203–235 (in Russian).
- Groups of a finite exponent with subgroups of a prime order, Algebra and Logika (1982), N 5, 553–618 (in Russian).
- Practical work in algebra, Moscow State Univ. Publ (1983) 92 pages, in Russian (jointly with a team of authors).
- 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).
- On a geometric method in combinatorial group theory, Proc. Int. Congress Math. 1(1983), 415–424.
- On abelian and central extensions of aspherical groups, Izvestia Vuzov, Matem. (1985), N 11, 48–60, in Russian (with I. S. Ashmanov).
- Varieties in which all finite groups are abelian, Matem. Sbornik, 126 (1985), N 1, 59–82 (in Russian).
- Subgroups of quasifinite groups, Uspekhi Matem. Nauk, 41 (1986), N 6, 169–170, in Russian (joint with G. S. Deryabina).
- The Neumanns – Shmel’kin’s theorem, Vestnik Mosk. Univ., Ser. Matem.(1986), N 6, 61–64 (in Russian).
- Collection of exercises in algebra, Moscow, Nauka (1987, 1995, 2001, 2006), 352 pages, in Russian (in a team of authors).
- 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). - The Mal’tsev problem on operations on groups, Trudy Sem. im. I. G. Petrovskogo, 14 (1989), 225–249 (in Russian)
- Geometry of defining relations in groups, Moscow, Nauka, 1989, 448 pages (in Russian, English translation by Kluwer Academic Publ., 1991).
- Thrifty embeddings of countable groups, Vestnik Mosk. Univ., Ser. Matem. (1989), N 2, 28–34 (in Russian).
- 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).
- Diagrams of homomorphisms of surface groups, Sibirsk. Matem. J., 30 (1989), N 6, 150–171 (in Russian).
- Some applications of graded diagrams in combinatorial group theory, London Math. Soc., Lecture Notes Ser., 160 (1990), 258–308 (with S. V. Ivanov).
- Embedding of countable periodic groups into 2-generator simple periodic groups, Ukrain. Matem. J., 43 (1991), N 7-8, 980–986 (in Russian).
- Hyperbolicity of groups with subquadratic isoperimetric inequality, Intern. J. of Algebra and Computation 1 (1991), N 3, 281–289 .
- Periodic quotients of hyperbolic groups, Matem. Sbornik., 182 (1991), N 4, 543–567 (in Russian).
- Almost every group is hyperbolic, Internat J. of Algebra and Comput., 2 (1992), N 1, 1–17.
- 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).
- Embedding of periodic groups into simple periodic groups, Ukrain. Matem. J., 44 (1992), N 6, 845–847 (in Russian).
- On residualing homomorphisms and G-subgroups of hyperbolic groups, Internat. J. of Algebra and Comput., 3 (1993), 1–44.
- On calculation of width in free groups, London Math. Soc., Lecture Notes Ser., 204 (1995), 255–258.
- A simplification of Golod’s example, Proc. 3rd Int. Conf. in Group Theory (Korea, Pusan, 1994), Walter de Gryuter (1995), 263–265.
- SQ-universality of hyperbolic groups, Matem. Sbornik, 186 (1995), N 8, 119–132 (in Russian).
- A group variety defined by a semigroup law, J. Austral. Math. Soc. (Series A) 60 (1996), 255–259 (with A.Storozhev).
- 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).
- Hyperbolic groups and their quotients of finite exponent, Trans. Amer. Math. Soc. 348 (1996) N 6, 2091–2138 (with S. V. Ivanov).
- 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).
- On the subgroup distortion in finitely presented groups, Matem. Sbornik, 188 (1997), N 11, 73–120 (in Russian).
- Some constructions relating to hyperbolic groups, London Math. Soc. Lecture Notes Ser., 252 (1998), 263–290 (joint with K. V. Mikhajlovskii).
- 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.
- The growth of finite subgroups in p-groups, London Math. Soc. Lect. Note Ser. 261 (1999), 579–595.
- 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).
- 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).
- Embeddings of relatively free groups into finitely presented groups, Contemp.Math., 264 (2000), 23–47 (joint with M.V.Sapir)
- On the Bass – Lubotzky question about quotients of hyperbolic groups, Journal of Algebra, 226 (2000), 807–817 .
- 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).
- 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).
- Comparison of products of the varieties of Lie algebras, Communications in Algebra, 29(2001), no. 9, 4267–4275 (with. A.L. Shmelkin).
- 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).
- Non-amenable finitely presented torsion-by-cyclic groups, Publ. Math. IHES, 96 (2003), no. 6, p.p. 43–169 (with M.V.Sapir).
- Self-normalization of free subgroups in the free Burnside groups,in “Groups, Rings and Lie Algebras”, Kluwer AP, 2003, 179–187.
- Conjugacy problem for groups and Higman embeddings, Electronic Res. Announc. of the AMS”, 9 (2003), 40–50 (with M.V.Sapir).
- Conjugacy problem and Higman embeddings, “Memoirs of the AMS” 170(2004), no. 804 p.p. vii+131 (with M.V.Sapir)
- 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)
- Groups with non-simply connected asymptotic cones, “Contemporary Mathematics”, 394 (2006),203–208 (with M.V.Sapir).
- Groups with small Dehn functions and bipartite chord diagrams, “Geometric and Functional Analysis”, 16 (2006), 1324–1376 (with M.V.Sapir).
- 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)
- Groups with quadratic-non-quadratic Dehn functions, “Intern. J. Algebra and Comput.”, 17(2007), no. 2, p.p. 401–419.
- 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)
- Large restricted Lie algebras, “Journal of Algebra”, 310 (2007), no. 1, 413–427 (with Yu.A.Bahturin).
- Linear automorphism groups of relatively free groups. “Turkish Journal of Mathematics”, 31(2007) (suppl., dedicated to the memory of Brian Hartley), 105–111.
- 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).
- Large groups and their periodic quotients. “Proc. of the AMS”, 136 (2008), no. 3, 753–759 (with D.V.Osin).
- On products of T-ideals in free algebras and free group algebras. “Journal of Pure and Applied Algebra”, 213(2009), no. 2, 259–263.
- Schreier rewriting beyond the classical setting. “Science in China”, Ser. A, Mathematics (Springer), 52 (2009), no.2, 231–243 (with Yu.A.Bahturin).
- Lacunarly hyperbolic groups. “Geometry and Topology”, 13(2009), no. 4, 2051–2140 (with D.V.Osin and M.V.Sapir).
- Periodic quotients of hyperbolic and large groups. “Groups, Geometry and Dynamics”, 3(2009), no.3, 423–452 (with A.Minasyan and D.Sonkin).
- On F
_{k}-like groups. “Algebra and Logic”, 48(2009), no.2, 140–146 (with M.V.Sapir). - Actions of maximal growth, “Proceedings of the London Math. Soc.” 101 (2010), no.1, 27–72 (with Yu.A.Bahturin).
- Filtrations and distortion in infinite-dimensional algebras, “Journal of Algebra”, 327 (2011), 251–291 (with Yu.A.Bahturin).
- Subgroup distortion in wreath products of cyclic groups, “Journal of Pure and Applied Algebra”, 215(2011) 2987–3004 (with Tara Davis).
- Space functions of groups, “Trans. Amer. Math. Soc”, 364 (2012), 4937–4985.
- 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).
- A quasi-isometric embedding theorem for groups,“Duke Math. Journal”, 162 (2013), no.9, 1621–1648 (with D.V.Osin).
- Space functions and space complexity of the word problem in semigroups, “Computational Complexity”, 22 (2013), no.4, pp. 771–830.
- On topologizable and non-topologizable groups, “Topology and its Applications”, 160 (2013), 2104-2120 (with Ant.A. Klyachko and D.V.Osin).
- On abelian subgroups of finitely generated metabelian groups,

“Journal of Group Theory”, 16 (2013), no.5, 695–705 (with V.H.Mikaelian). - C
^{*}-simple groups without free subgroups, “Groups, Geometry and Dynamics”, 8 (2014), 933-983. (with D.V.Osin). - Growth of subalgebras and subideals in free Lie algebras, “Journal of Algebra” 422 (2015), 277-305 (with Yu.A.Bahturin).
- Relative subgroup growth and subgroup distortion, “Groups, Geometry and Dynamics”, 9 (2015), no.1, 237-273 (with Tara Davis).
- 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).
- 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).
- On pairs of finitely generated subgroups in free groups, “Proceedings AMS”, 143 (2015), 4177-4188.
- Diagonal bi-acts over semigroups with finiteness conditions, “Semigroup Forum”, 91 (2015), no. 2, 538-542 (with I.B. Kozhukhov).
- Constructions of torsion-free countable, amenable, weakly mixing groups, L’Enseignement Mathematique” (2), 61 (2015), 321-342; (with R. Grigorchuk and R. Kravchenko).
- On Kaluzhnin – Krasner’s embeddings of groups, Algebra Discrete Math. 19 (2015), no. 1, 77-86.
- Embedding construction based on amalgamations of group relators, “Journal of Topology and Analysis”, 8 (2016), no. 1, 1-24.
- Subnormal subgroups in free groups, their growth and co-growth, ”Math. Proc. Cambridge Phil. Soc.”, 163 (2017), no. 3, 499-531.
- On flat submaps of maps of non-positive curvature, Accepted to ”Transactions of the American Mathematical Society”.

arXiv:1702.08205, 2017 (with M. Sapir). - On cardinality of sets of relators for the group F/∏[N
_{i},N_{j}], “Fundamental and Applied Mathematics”, accepted (with O.V. Kulikova). - Polynomially-bounded Dehn functions of groups, “Journal of Combinatorial Algebra”, 1 – 123, DOI 10.41J1/JCA/2-y-z.
- Conjugacy problem in groups with quadratic Dehn function,

arXiv.math.1809.00280, 83pp. (with M.V. Sapir).