2005 | 2004 | 2003 | 2002 | 2001 | 2000 | 1999 | 1998 | 1997 | 1996 | 1995 and earlier 2005
Fully residually free groups and
graphs labeled by infinite words (with V. Remeslennikov
and D. Serbin), to
appear in Internat. J. Algebra and Comput. A practical attack on some braid
group based cryptographic protocols (with V. Shpilrain
and A. Ushakov). CRYPTO 2005, Lecture Notes Comp. Sci,
3621 (2005), 86-96. On positive theories of groups with
regular length functions (with B. Khan and D. Serbin). Algebraic geometry over groups III:
Elements of model theory (with A. Kvaschuk and V. Remeslennikov). J. of
Algebra, 288 (2005), no. 1,
78-98. [.pdf] Finitary Andrews-Curtis conjecture (with A.V. Borovik and A. Lubotzky), submitted. We formulate a generalized AC-conjecture for an arbitrary group and prove that it holds for every finite group. In fact, there are no counter examples to the generalized AC conjecture so far. Such examples would shed some light on potential counterexamples to the original AC conjecture. Pattern Recognition and Minimal
Words in Free Groups of Rank 2 (with
Robert M. Haralick and Alexei D. Miasnikov), submitted. [.pdf] We describe a linear time probabilistic algorithm to recognize Whitehead minimal elements (elements of minimal length in their automorphic orbits) in free groups of rank 2. Moreover, for a non-minimal element the algorithm gives an automorphism that will most likely reduce the length of the element. This method is based on linear regression and pattern recognition techniques. I did not believe this myself first, until I've seen it working with my own eyes. Effective JSJ decompositions (with O. Kharlampovich), Contemp.
Math., 378, Amer. Math. Soc., Regular free length
functions on Lyndon's free Z[t]-group F^Z[t] (with V. Remeslennikov
and D. Serbin), Contemp. Math., 378, Amer. Math. Soc., The conjugacy
problem in amalgamated products I: regular elements and black holes (with
A. Borovik and V. Remeslennikov).
Preprint. The conjugacy
problem in amalgamated products II: generic complexity (with A. Borovik and V. Remeslennikov). Preprint. Big powers and free
constructions (with A. Kvaschuk), submitted. Algorithmic stratification
of the conjugacy problem in Miller’s groups (with A. Borovik and V. Remeslennikov). Preprint. [.pdf] Groups whose universal
theory is axiomatizable by quasi-identities (with
B. Fine, A.M. Gaglione
and D. Spellman), to appear in J.
of Group Theory. Algebraic geometry over free
groups: lifting solutions into generic points (with O. Kharlampovich),
Contemp. Math., 378, Amer.
Math. Soc., Implicit function theorems over
free groups (with O. Kharlampovich). J. of Algebra, 290
(2005), no. 1, 1-203. [.pdf] Quotient tests and Gröbner bases (with M. Kreuzer,
G. Rosenberger and A. Ushakov), submitted. [.pdf] The halting problem is
almost always decidable (with J. Hamkins), Preprint. [.pdf] Quotient tests and random
walks in computational group theory (with A. Borovik), submitted. [.pdf] The conjugacy
problem in HNN-extensions I: regular elements, black holes and generic complexity (with A. Borovik and V. Remeslennikov). Preprint. Isomorphism problem for
finitely generated fully residually free groups (with I.
Bumagin and O. Kharlampovich), submitted.[.pdf] Exponential extensions of
groups (with O. Kharlampovich, V. Remeslennikov and D. Serbin), to appear in J.
of Group Theory. [.pdf] One variable equations over hyperbolic groups (with A. Kvaschuk). Preprint. On the Hanna Newmann Conjecture (with T.Jitsukawa
and B.Khan). Preprint.
[.pdf] Elementary theory of free
non-abelian groups. The Tarski
problem. (with O. Kharlampovich). Preprint. Heuristics for Whitehead
Minimization Problem (with R.M. Haralick and A.D. Miasnikov). Preprint. Theorems on hierarchy in
generalized recursion theory (with V. Belyaev). Preprint. Average-case complexity and
decision problems in group theory (with I. Kapovich,
P. Schupp and V. Shpilrain),
Adv. Math. 190 (2005), no.2, 190-205. [.pdf] Foldings, graphs of groups and the membership problem (with I.Kapovich and R.Weidmann), Internat. J. Algebra Comput. 13 (2005), no. 1, 95-128. [.pdf] 2004
Subgroups of fully
residually free groups: algorithmic problems (with O. Kharlampovich,
V. Remeslennikov and D. Serbin). Group theory, statistics, and cryptography, 63-101, Contemp.
Math., 360, Amer. Math. Soc., Pattern Recognition Approaches to
Solving Combinatorial Problems in Free Groups (with Robert M.
Haralick and Alexei D. Miasnikov), Contemp. Math., 349, Amer. Math. Soc., In this survey paper we present some pattern recognition techniques that can be used in studying free groups. As an illustration we apply these methods to Whitehead minimization problem. Whitehead method and Genetic Algorithms (with
Alexei D. Miasnikov) Contemp. Math., 349,
Amer. Math. Soc., We describe a genetic Whitehead's algorithm for finding minimal elements (elements of minimal length in automorphic orbits) in arbitrary free groups. The classical Whitehead's algorithm is extremely inefective for free groups of big ranks, but this genetic version of it works all right. Also we formulate several mathematical conjectures that came out of our experiments. Discriminating and
co-discriminating groups (with P. Shumyatsky). J. Group Theory 7 (2004), no. 1, 135-142. [.pdf] One Variable Equations in
free groups via context free languages (with R. Gilman). Computational
and experimental group theory, 83-88, Contemp. Math., 349, Amer. Math. Soc., 2003
Elementary theory of free
groups (with B.Fine, A.M.Gaglione
and D.Spellman),
Proc. Of the
Oxford/St. Andrews Conf. on Combinatorial Group Theory, Note Ser. 304 (2003), 197-231. Multiplicative measures on
free groups (with A. Borovik and V. Remeslennikov). Internat. J. Algebra Comput. 13 (2003),
no. 6, 705-731. [.pdf] The Andrews-Curtis
Conjecture and Black Box Groups (with A.V. Borovik
and E.I. Khukhro). Internat. J. Algebra Comput., 13 (2003), no. 4, 415-436. [.pdf] We introduce Andrews-Curtis graphs of groups and discuss their connection with black-box groups and the replacement algorithm, study AC conjecture for finite groups, and describe possible attacks on AC conjecture via finite groups. Automorphic orbits in free groups (with V.Shpilrain).
J. of Algebra, 269 (2003), no. 1, 18-27. [.pdf] Generic-case complexity and
decision problems in group theory (with Schupp and V.Shpilrain). J. of Algebra, 264 (2003), 665-694. [.pdf] 2002
Discriminating completions
of hyperbolic groups (with G. Baumslag and V. Remeslennikov). Geom. Dedicata 92 (2002), 115-143. [.pdf] Measuring sets in infinite
groups (with A. Borovik and V. Shpilrain).
Computational
and statistical
group theory ( Amer. Math. Soc., Open problems in
combinatorial group theory. Second edition (with G. Baumslag
and V. Shpilrain).
Combinatorial
and geometric group theory (New York, 2000/Hoboken, NJ, 2001), 1-38, Contemp.
Math., 296, Amer. Math. Soc., On the Andrews-Curtis
equivalence (with A.D. Miasnikov and V. Shpilrain).
Combinatorial and geometric
group theory (New York, 2000/Hoboken, NJ, 2001), 183-198. Contemp. Math., 296, Amer. Math. Soc., We construct various examples of balanced presentations of the trivial group and show that some of them satisfy AC conjecture. We also consider AC-equivalence in metabelian groups and reveal some interesting connections of it with well-known problems in K-theory. Stallings foldings and subgroups of free groups (with (2002), 608-668. 2001
Discriminating groups (with
B. Fine, A.M. Gaglione and D. Spellman). J. of Group Theory 4 (2001), no. 4, 463-474. [.pdf] Implicit function theorem
over free groups and genus problem (with O. Kharlampovich). Knots, braids, and mapping class groups---papers dedicated to
Joan S. Birman (New York, 1998), 77-83, AMS/IP Stud. Adv.
Math., 24, Amer. Math. Soc., Balanced presentations of
the trivial group on two generators and the Andrews-Curtis conjecture (with A.D. Miasnikov). Groups and computation, III (Columbus, OH, 1999), 257-263. Ohio State Univ. Math.
Res. Inst. Publ. 8, We proved that every balanced presentation on two generators of the trivial group satisfies the AC conjecture. 2000
Discriminating and
co-discriminating groups (with G. Baumslag and V. Remeslennikov). J. Group Theory 3 (2000), no. 4, 467–479. [.pdf] Algebraic geometry 2:
logical foundations (with V. Remeslennikov). J. of Algebra 234 (2000), 225-276. [.pdf] Centroids of groups (with Algebraic
geometry over groups (with G. Baumslag and V. Remeslennikov).
Algorithmic
problems in groups and semigroups
(Lincoln, NE, 1998), 35-50, Trends Math., Birkhäuser Aspects of the theory of
free groups (with K. Bencsath, B. Fine, A. Gaglione, G. Rosenberger and D.
Spellman). Algorithmic problems in
groups and semigroups ( NE,
1998), 35--50, Trends Math., Birkhäuser
Boston, 1999
Malnormality is decidable in free groups (with G.Baumslag
and V.Remeslennikov). Internat. Journal Algebra Comput. 9 (1999), no.6, 687-692. [.pdf] Open problems in
combinatorial group theory (with G. Baumslag and V.
Shpilrain). Groups,
languages and geometry (South Hadley, MA, 1998), 1-27, Contemp.
Math., 250, Amer.
Math. Soc., Equations over Q-completions
of hyperbolic groups (with O. Kharlampovich and E. Lyutikova). Trans. Amer. Math. Soc. 351 (1999), no. 7, 2961-2978. Algebraic geometry over and V. Remeslennikov). J. of Algebra 219 (1999), 16-79. [.pdf] Description of fully
residually free groups and irreducible affine varieties over a free group (with O. Kharlampovich). Summer School in Group Theory in CRM Proc. Lecture Notes, 17,
Amer. Math.
Soc., 1998
A classification of fully residually free groups of rank three
or less (with A. Gaglione, B. Fine, G. Rosenberger and D.Spellman). J. of Algebra, 200 (1998), no. 2, 571-605. Irreducible affine varieties
over a free group. II: Systems in
triangular quasi-quadratic form and description of residually free groups (with O. Kharlampovich). J.
of Algebra 200 (1998), no. 2, 517--570. [.pdf] Irreducible affine varieties
over a free group. I: Irreducibility
of quadratic equations and Nullstellensatz (with O. Kharlampovich). J.
of Algebra 200 (1998), no. 2,
472-516. Equations in free a Q-group
(with O. Kharlampovich). Trans. Amer. Math. Soc. 350 (1998), no. 3, 947-974. [.pdf] Hyperbolic groups and free
constructions (with O. Kharlampovich). Trans. Amer. Math. Soc. 350 (1998),
no. 2, 571-613. [.pdf] 1997
Two theorems about equationally Noetherian groups
(with G. Baumslag and V. Romankov). J, of Algebra 194 (1997),
654-613. [.pdf] Formal power series representations
of free exponential groups (A.M. Gaglione, V.N. Remeslennikov, D. Spellman). Comm.
Algebra, 25 (1997), no. 2,
631-648. 1996
Exponential groups 2:
extension of centralizers and tensor completion of CSA-groups (with
V. Remeslennikov). Internat.
J. Algebra Comput. 6 (1996),
no. 6, 687-711. [.pdf] Length functions on free
exponential groups (with V. Remeslennikov). Proc. IITPM SO RAN
26, 1995 and earlier
Length functions on free
exponential groups (with V. Remeslennikov). Proc.of Intern. Conference
in Analysis and Geometry, CSA groups and separated
free constructions (with D. Gildenhuys and O. Kharlampovich). Bull. Austr.
Math. Soc. 52 (1995), no. 1, 63-84. [.pdf] Logical languages and axioms for groups with a length function (with O. Kharlampovich and V. Remeslennikov). Proc. Inst. Appl. Math. Russian Acad. Sci. 20 (1995), 1-8. Exponential groups I:
foundations of the theory and tensor completions (with V. Remeslennikov). Siberian Math. J.. 35 (1994),
no. 5, 1106-1118. Aproaches to the theory of computability (with Logika, 1994, v.4. Recursively enumerable
degrees over the reals (with V. Belyaev).
Proc. of
Intern. Algebraic
Conf., Model-theoretic problems of
algebra. Dissertation, VINITI, Admissible sets in group
theory (with V.Remeslennikov). Algebra i logika, 3 (1992). Weak second order logic in
group theory (with V.Remeslennikov). Contemp. Math. 131
(1992), no. 2, 273-277. Logic of finite types in group
theory (with V.Remeslennikov). Bull. Siberian Math. Soc., Model theory of bilinear
mappings. Siberian J. Math., 31 (1990), no. 3, 94-108. Invariants of bilinear
mappings. Siberian J. Math., 31 (1990), no. 1, 104-115. Model-theoretical problems
in group theory (with V.Remeslennikov). Problems of Algebra 4, Modules over local ring. Siberian J. Math.,
30 (1989), no. 3, 72-83. Structure of models and
criteria of decidability of complete theories of finite-dimensional algebras
(with V.Remeslennikov). Izvest. Akademii Nauk USSR, ser.math 53 (1989), no. 2., 379-397. Recursive p-adic numbers and elementary theories of finitely
generated pro-p-groups (with
V.Remeslennikov). Izvest.
Akademii Nauk USSR, ser.math 30 (1988), no.3. Abstract isomorphisms
and elementary theories of finite dimensional algebras and unipotent groups. Doklady
Akademii Nauk Free operator groups with
length function and finitely generated group of operators. Computable invariants of
algebraic structures., Elementary group equivalence
with the integral length function (with V.Remeslennikov). Stable torsion-free rings
and nilpotent groups. VII Generalized Nielsen
transformations and trivial groups. Math.
Notes, 5 (1984), no. 4, 491- 495. Finite-dimensional algebras
and k-groups of finite rank. Contemp.
Math., 33 (1984), 436- 453. Definability of Mal'cev bases and elementary properties of finite
dimensional algebras. II (with
V.Remeslennikov). Siberian J. Math.,
24 (1982), no. 2, 97-113. Definability of Mal'cev bases and elementary properties of finite
dimensional algebras. I (with
V.Remeslennikov). Siberian J. Math.,
23 (1982), no. 5, 152-167. Elementary properties of
powered nilpotent groups (with V.Remeslennikov). Doklady Akademii Nayuk 258 (1981), no.
5, 1056-1059. Isomorphism and elementary
properties of powered nilpotent groups (with
V.Remeslennikov). Proc.Math.Institute 2, Nauka, On the approximability
of groups of outer automorphisms of free groups of
finite rank. Algebra and Logic, 20 (1981), no.3, 291-299. |