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**THE MOST IMPORTANT PUBLICATIONS**

O. Kharlampovich,
A. Myasnikov, Limits of relatively hyperbolic
groups and Lyndon's completions, Journal of the European Math.
Soc., 2010, accepted

O. Kharlampovich, A. Vdovina, Linear estimates for solutions of quadratic equations in free groups, 15 pages, 2011, accepted to the IJAC

O. Kharlampovich,
A. Mohajeri, Approximation of Geodesics in
Metabelian Groups, 13 pages,
2011, acceptad to the IJAC.

O. Kharlampovich, A. Myasnikov, D. Serbin, Groups with free regular length functions in ${\bf Z}^n$, Transactions of the AMS, 2010, accepted.

O. Kharlampovich, B. Khoussainov, and A. Miasnikov, From automatic structures to automatic groups, 35 pages, 2011, submitted.

I. Bumagin, O. Kharlampovich, ${\bf Z}^n$-free groups are CAT(0), 2011, Arxiv, 19 pages, submitted

O. Kharlampovich, I. Lysenok, A. Myasnikov, N. Touikan, Quadratic equations over free groups are NP-complete, TOCS (Teor. Comp. Syst.), 10, 2008.

O. Kharlampovich, A. Myasnikov, V. Remeslennikov, D. Serbin, Exponential extensions of groups. J. Group Theory 11 (2008), no. 1,119--140.

- I. Bumagin,O. Kharlampovich, A. Miasnikov, Isomorphism problem for fully residually free groups , J. Pure and Applied Algebra, Volume 208, Issue 3, March 2007, Pages 961-977.
- O. Kharlampovich, A. Miasnikov, Elementary theory of free nonabelian groups (paper 5 on the theory of a free group) , J.Algebra, 302, Issue 2, 451-552, 2006. 2002 version, first 1999 version.
- O. Kharlampovich, A. Miasnikov, Effective JSJ decompositions (paper 4 on the theory of a free group), Contemp.Math. AMS, Algorithms,Languages, Logic (Borovik, ed.), CONM/ 378, 2005, 87-212 (Math GR/0407089).
- O. Kharlampovich, A. Miasnikov, Implicit function theorem over free groups and genus problem Proceedings of the Birmanfest, AMS/IP Studies in Advanced Mathematics, v. 24, 2001, 77--83.
- O. Kharlampovich, A. Myasnikov, Algebraic geometry for free groups: lifting solutions into generic points, Contemp.Math. AMS, Algorithms, Languages, Logic (Borovik, ed.), CONM/ 378, 2005, 213-318 (Math GR/0407110).
- O. Kharlampovich, A. Myasnikov, V. Remeslennikov, D. Serbin, Subgroups of fully residually free groups: algorithmic problems, Contemp. Math. series of the AMS, Group theory, Statistics and Cryptography, 360 (2004).
- O. Kharlampovich, Equations over fully residually free groups . Sections "Auxiliary results", "Projective images", Theorem 2 from the 1999 version of this paper were moved into paper 5 ("Elementary theory..."), all the other results appeared in the paper "Effective JSJ decompositions".
- O. Kharlampovich, A. Myasnikov, Implicit function theorem over free groups , (paper 3 on the theory of a free group, Math. GR/0312509), Journal of Algebra, vol 290/1, pp. 1--203, 2005. 2000 version. The last section from the 1999 version of this paper was moved into paper 5 ("Elementary theory...").
- O. Kharlampovich, E. Lioutikova and A.
Myasnikov,
Equations in the
**Q**-completion of a torsion-free hyperbolic group, Transactions of the A.M.S., V. 351, No. 4, 1999, 20 pages. - O. Kharlampovich and A. Myasnikov,Tarski's problem about the elementary theory of free groups has a positive solution, PDFERA-AMS, V.4, 1998, 101--108.
- O. Kharlampovich and A. Myasnikov, Equations
in
a free
**Q**-group, Transactions of the A.M.S., V. 350, No. 3, March 1998, 947--974. - O. Kharlampovich and A. Myasnikov, Hyperbolic groups and free constructions, Transactions of the A.M.S., V. 350, No. 2, Feb. 1998, 571--613.
- O. Kharlampovich, A. Myasnikov , Irreducible affine varieties over a free group. I: Irreducibility of quadratic equations and Nullstellensatz (paper 1 on the theory of a free group), J. Algebra, V. 200, 472--516 (1998).
- O. Kharlampovich, A. Myasnikov , Irreducible affine varieties over a free group. II: Systems in row-echelon form and description of residually free groups (paper 2 on the theory of a free group), J. Algebra, V. 200, 517--570 (1998).
- O. Kharlampovich, A. Myasnikov, V. Remeslennikov, Logical languages and axioms for groups with a length function, Russian academy of sciences, Siberian division, Preprint 20, Omsk 1995.
- O. Kharlampovich and M. Sapir, Algorithmic problems in varieties, a survey, International Journal of Algebra and Computation, (1995), # 12, 379--602.
- D. Gildenhuys, O. Kharlampovich, A. Myasnikov, CSA groups and separated free constructions, Bull. Austral. Math. Soc., Vol. 52 (1995), 63--84.
- O. Kharlampovich, The word problem for the Burnside groups, Journal of Algebra, 173, (1995), 613--621.
- D. Gildenhuys, S. Ivanov and O. Kharlampovich, On a series of 1-relator pro-p-groups, (13 pages), Proceedings of The Royal Society of Edinburgh, Vol. 124A, (1994), 1199--1207.
- O. Kharlampovich and D. Gildenhuys, The word problem for some varieties of solvable Lie algebras, International Journal of Algebra and Computation, Vol.4, No.3(1994), 481--491.
- O. Kharlampovich and D. Gildenhuys, Varieties of Lie algebras with solvable word problem, Communications in Algebra, Vol.21, No.10 (1993), 3571--3609.
- O. Kharlampovich and D. Gildenhuys, Identities
in
the variety
of center-by-N
_{2}A Lie algebras, International Journal of Algebra and Computation, v.1, #4 (1991), 493--521. - O. Kharlampovich, The word problem for solvable Lie algebras; a boundary between solvability and unsolvability, Contemporary Mathematics, v.131, (Part 2)(1992), 53--57.
- O. Kharlampovich, The word problem for solvable groups and Lie algebras, MSRI Publications by Springer-Verlag 23, (Algorithms and Classification in Combinatorial Group Theory, MSRI, Berkeley, CA) (1991), 61--69.
- O. Kharlampovich, The word problem for solvable groups and Lie algebras, Math. USSR Sbornik 67, 2 (1990), 489--525.
- O. Kharlampovich, Finitely presented solvable groups and Lie algebras with unsolvable word problem, Mat. Notes 46, 3-4 (1990), 731--738.
- O. Kharlampovich and M. Sapir, The word problem in varieties of Lie and associative algebras, Soviet Math. Iz. Vuz. 6 (1989), 76--84.
- O. Kharlampovich, Minimal varieties of groups and Lie algebras with unsolvable word problem, in ``Siberian School on Varieties of Algebraic Systems'', Barnaul (1988), 72--75.
- O. Kharlampovich, Equality problem in the variety $ZN_2A$, Iz. Vuz. Mat. No.11 (1988), 21--33.
- O. Kharlampovich, The word problem for subvarieties of the variety N2A, Algebra i Logika 26, 4 (1987), 258--285.
- O. Kharlampovich, I. Mel'nichuk and M. Sapir, The word problem in the varieties of semigroups, rings and Lie algebras, Sib. Math. J. 27, 6 (1986), 144--156.
- O. Kharlampovich, Lyndon's condition for solvable Lie algebras, Soviet Math. Iz. Vuz. 9 (1984), 50--59.
- O. Kharlampovich, The undecidability of the universal theory of some classes of Lie rings, in "Dep. VINITI, #5469-83", Sverdlovsk (1983), 2--17.
- O. Kharlampovich, The universal theory of the class of finite nilpotent groups is unsolvable, Mat. Zametki 33, 4 (1983), 499--516.
- O. Kharlampovich, A finitely presented solvable group with unsolvable word problem, Izvest. Ak. Nauk, Ser. Mat. (Soviet Math., Izvestia) 45, 4 (1981), 852--873.
- O. Kharlampovich and A. Myasnikov, Implicit function theorem for free groups.
- O. Kharlampovich and A. Myasnikov, Equations over fully residually free groups.
- O. Kharlampovich and A. Myasnikov, Implicit function theorem over free groups and genus problem.

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