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Bardakov, Valeriy Georgievich

Statistics Math-Net.Ru
Total publications: 40
Scientific articles: 38
Presentations: 4

Number of views:
This page:5465
Abstract pages:15768
Full texts:3953
References:1639
Associate professor
Doctor of physico-mathematical sciences
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
E-mail:
Keywords: group theory; knot theory; braid groups; automorphism groups; permutation groups; width of verbal subgroups; equations in groups; partial differential equation; multidimensional inverse problems; evolution equations; integral geometry; systems of kinetic equations.

Subject:

It is proved that any verbal subgroup $V(B_n)$ of braid group $B_n$, $n>2$, defined by a finite set of words $V$ has infinite width. Similar result is proved for some Artin groups. We investigate decompositions of automorphisms of various free modules into products of transvections and dilations. In particular, as a corollary, we obtain that for $n>2$ the width of the spetial linear group $SL_n(Z)$ over ring of integer $Z$, with respect to the set of commutators, does not exceed 10. It is shown that for any integers $k>3$ and $m>0$ any permutation in the alternating group $A_{km}$ of degree $km$ can be expressed as the product of two permutations each of them has $m$ cycles of length $k$ in its cycle decomposition. This proves a conjecture by J. L. Brenner and R. J. Evans. It is proved that if in the HNN-extension $G^*$, the subgroups $A$ and $B$ are distinct from the base group $G$, then every subgroup $V(G^*)$ defined by a finite proper set $V$ of words has infinite width relative to $V$. Similar results are proved for groups with one relation and number generations greater 2 and for some free produts with amalgamations. It is described a new algorithm for calculating the commutator length in free groups and some equations in free groups are investigated. It is proved that there exist continuum many non-isomorphic two-generated groups which each possess a regularly exhausting sequence with polynomial growth and which are but not groups with polynomial growth.

Biography

Graduated from Faculty of Mathematics and Mechanics of Novosibirsk state University in 1963 (department of Algebra and Logic). Ph.D. thesis was defended in 1994. A list of my works containes nearly 50 titles. Since 1995 I have led the algebraic seminar "Evarist Galua" at NSU. Since 2000 I and A. Yu. Vesnin have led the special course "Algebraic methods in knot theory" at NSU.

In 1993 I was awarded the Prize of M. I. Kargapolov for young mathematicians for solving problems from "Kourovka Notebook".

   
Main publications:
  • Bardakov V. G. Two inverse problems for a system of quantum kinetic equations // J. Inv.Ill-Posed Problems, 7, 2(1998), 105–119.

https://www.mathnet.ru/eng/person8773
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/328717

Publications in Math-Net.Ru Citations
2024
1. V. G. Bardakov, T. A. Kozlovskaya, D. V. Talalaev, “$n$-valued quandles and associated bialgebras”, TMF, 220:1 (2024),  25–43  mathnet  mathscinet; Theoret. and Math. Phys., 220:1 (2024), 1080–1096  scopus
2023
2. V. G. Bardakov, T. A. Kozlovskaya, “Multivalued groups and Newton polyhedron”, Sib. Èlektron. Mat. Izv., 20:2 (2023),  1590–1596  mathnet
3. V. G. Bardakov, D. V. Talalaev, “Extensions of Yang–Baxter sets”, TMF, 215:2 (2023),  176–189  mathnet  mathscinet; Theoret. and Math. Phys., 215:2 (2023), 609–621  scopus 1
2020
4. V. G. Bardakov, T. R. Nasybullov, “Multi-switches, representations of virtual braids, and invariants of virtual links”, Algebra Logika, 59:4 (2020),  500–506  mathnet; Algebra and Logic, 59:4 (2020), 341–345  isi  scopus 5
5. V. G. Bardakov, M. V. Neshchadim, “Lower central series of Baumslag–Solitar groups”, Algebra Logika, 59:4 (2020),  413–431  mathnet; Algebra and Logic, 59:4 (2020), 281–294  isi  scopus 3
2017
6. V. G. Bardakov, M. V. Neshchadim, “A representation of virtual braids by automorphisms”, Algebra Logika, 56:5 (2017),  539–547  mathnet; Algebra and Logic, 56:5 (2017), 355–361  isi  scopus 8
7. V. G. Bardakov, Yu. A. Mikhalchishina, M. V. Neshchadim, “Virtual link groups”, Sibirsk. Mat. Zh., 58:5 (2017),  989–1003  mathnet  elib; Siberian Math. J., 58:5 (2017), 765–777  isi  elib  scopus 12
8. V. G. Bardakov, M. V. Neshchadim, “Knot groups and nilpotent approximability”, Trudy Inst. Mat. i Mekh. UrO RAN, 23:4 (2017),  43–51  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 304, suppl. 1 (2019), S23–S30  isi 3
2016
9. V. G. Bardakov, M. V. Neshchadim, “Subgroups, automorphisms, and Lie algebras related to the basis-conjugating automorphism group”, Algebra Logika, 55:6 (2016),  670–703  mathnet; Algebra and Logic, 55:6 (2017), 436–460  isi  scopus 3
10. V. G. Bardakov, R. Mikhailov, V. V. Vershinin, J. Wu, “On the pure virtual braid group $PV_3$”, Comm. Algebra, 44:3 (2016),  1350–1378  mathnet  mathscinet  isi  scopus 9
2015
11. V. G. Bardakov, M. V. Neshchadim, “An Example of a Nonlinearizable Quasicyclic Subgroup in the Automorphism Group of the Polynomial Algebra”, Mat. Zametki, 98:2 (2015),  180–186  mathnet  mathscinet  elib; Math. Notes, 98:2 (2015), 210–215  isi  scopus
12. V. Bardakov, K. Gongopadhyay, M. Singh, A. Vesnin, J. Wu, “Some problems on knots, braids, and automorphism groups”, Sib. Èlektron. Mat. Izv., 12 (2015),  394–405  mathnet 4
13. V. G. Bardakov, M. S. Petukhova, “On potential counterexamples to the problem of zero divisors”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 15:3 (2015),  30–50  mathnet; J. Math. Sci., 221:6 (2017), 778–797 2
2014
14. V. G. Bardakov, V. V. Vershinin, J. Wu, “On Cohen braids”, Trudy Mat. Inst. Steklova, 286 (2014),  22–39  mathnet  elib; Proc. Steklov Inst. Math., 286 (2014), 16–32  isi  elib  scopus 2
2013
15. V. G. Bardakov, A. A. Simonov, “Rings and groups of matrices with a nonstandard product”, Sibirsk. Mat. Zh., 54:3 (2013),  504–519  mathnet  mathscinet; Siberian Math. J., 54:3 (2013), 393–405  isi  scopus 6
16. V. G. Bardakov, T. R. Nasybullov, M. V. Neshchadim, “Twisted conjugacy classes of the unit element”, Sibirsk. Mat. Zh., 54:1 (2013),  20–34  mathnet  mathscinet; Siberian Math. J., 54:1 (2013), 10–21  isi  scopus 8
2012
17. V. G. Bardakov, R. Mikhailov, V. V. Vershinin, J. Wu, “Brunnian braids on surfaces”, Algebr. Geom. Topol., 12:3 (2012),  1607–1648  mathnet  mathscinet  zmath  isi  scopus 6
18. Yu. E. Anikonov, N. B. Aiupova, V. G. Bardakov, V. P. Golubyatnikov, M. V. Neshchadim, “Inversion of mapping and inverse problems”, Sib. Èlektron. Mat. Izv., 9 (2012),  382–432  mathnet 11
19. V. G. Bardakov, M. V. Neshchadim, “On the number of relations in free products of abelian groups”, Sibirsk. Mat. Zh., 53:4 (2012),  741–751  mathnet  mathscinet; Siberian Math. J., 53:4 (2012), 591–599  isi  scopus
2007
20. V. G. Bardakov, R. V. Mikhailov, “On the residual properties of link groups”, Sibirsk. Mat. Zh., 48:3 (2007),  485–495  mathnet  mathscinet  zmath  elib; Siberian Math. J., 48:3 (2007), 387–394  isi  elib  scopus 8
21. V. G. Bardakov, O. V. Bryukhanov, “On linear representations of some extensions”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 7:3 (2007),  45–58  mathnet 1
2006
22. V. G. Bardakov, “Braid Groups in Genetic Code”, Algebra Logika, 45:2 (2006),  131–158  mathnet  mathscinet  zmath  elib; Algebra and Logic, 45:3 (2006), 75–91  elib  scopus 1
2005
23. V. G. Bardakov, “Virtual and welded links and their invariants”, Sib. Èlektron. Mat. Izv., 2 (2005),  196–199  mathnet  mathscinet  zmath 10
24. V. G. Bardakov, “Linear representations of the group of conjugating automorphisms and the braid groups of some manifolds”, Sibirsk. Mat. Zh., 46:1 (2005),  17–31  mathnet  mathscinet  zmath; Siberian Math. J., 46:1 (2005), 13–23  isi 7
2004
25. V. G. Bardakov, “On D. I. Moldavanskii's question about $p$-separable subgroups of a free group”, Sibirsk. Mat. Zh., 45:3 (2004),  505–509  mathnet  mathscinet  zmath; Siberian Math. J., 45:3 (2004), 416–419  isi 7
2003
26. V. G. Bardakov, “Structure of a Conjugating Automorphism Group”, Algebra Logika, 42:5 (2003),  515–541  mathnet  mathscinet  zmath  elib; Algebra and Logic, 42:5 (2003), 287–303  scopus 21
27. V. G. Bardakov, A. Yu. Vesnin, “A Generalization of Fibonacci Groups”, Algebra Logika, 42:2 (2003),  131–160  mathnet  mathscinet  zmath; Algebra and Logic, 42:2 (2003), 73–91  scopus 23
28. V. G. Bardakov, “On a relation between the Arikonov-Amirov identity and the Pestov identity”, Sib. Zh. Ind. Mat., 6:2 (2003),  15–25  mathnet  mathscinet  zmath 2
2002
29. V. G. Bardakov, “Solution of the inverse problem for a matrix transport equation”, Sib. Zh. Ind. Mat., 5:3 (2002),  35–52  mathnet  mathscinet  zmath
2001
30. V. G. Bardakov, “Construction of a Regularly Exhausting Sequence for Groups with Subexponential Growth”, Algebra Logika, 40:1 (2001),  22–29  mathnet  mathscinet  zmath; Algebra and Logic, 40:1 (2001), 12–16  scopus 2
2000
31. V. G. Bardakov, “Computation of commutator length in free groups”, Algebra Logika, 39:4 (2000),  395–440  mathnet  mathscinet  zmath; Algebra and Logic, 39:4 (2000), 224–251  scopus 9
32. V. G. Bardakov, “The classification of differential equations with two independent variables on the basis of the principal part”, Differ. Uravn., 36:2 (2000),  187–197  mathnet  mathscinet; Differ. Equ., 36:2 (2000), 213–223
1998
33. V. G. Bardakov, “On orthogonal bases of rational lattices”, Sibirsk. Mat. Zh., 39:6 (1998),  1236–1250  mathnet  mathscinet  zmath; Siberian Math. J., 39:6 (1998), 1067–1079  isi
1997
34. V. G. Bardakov, “On the width of verbal subgroups of some free constructions”, Algebra Logika, 36:5 (1997),  494–517  mathnet  mathscinet 18
35. V. G. Bardakov, “Even permutations not representable in the form of a product of two permutations of given order”, Mat. Zametki, 62:2 (1997),  169–177  mathnet  mathscinet  zmath; Math. Notes, 62:2 (1997), 141–147  isi 1
1995
36. V. G. Bardakov, “On the decomposition of automorphisms of free modules into simple factors”, Izv. RAN. Ser. Mat., 59:2 (1995),  109–128  mathnet  mathscinet  zmath; Izv. Math., 59:2 (1995), 333–351  isi 2
1993
37. V. G. Bardakov, “Factorization of even permutations into two factors of given cyclic structure”, Diskr. Mat., 5:1 (1993),  70–90  mathnet  mathscinet  zmath; Discrete Math. Appl., 3:4 (1993), 385–406 1
1992
38. V. G. Bardakov, “On the theory of braid groups”, Mat. Sb., 183:6 (1992),  3–42  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 76:1 (1993), 123–153  isi 11

2022
39. Yu. L. Ershov, S. S. Goncharov, V. D. Mazurov, V. G. Bardakov, N. V. Bayanova, V. V. Bludov, L. A. Bokut', S. V. Varaksin, A. V. Vasil'ev, E. P. Vdovin, M. A. Grechkoseeva, A. V. Zenkov, P. S. Kolesnikov, L. L. Maksimova, I. A. Mal'tsev, A. S. Morozov, N. A. Peryazev, A. G. Pinus, K. N. Ponomarev, A. M. Popova, V. N. Remeslennikov, V. A. Roman'kov, N. S. Romanovskii, E. I. Timoshenko, V. A. Churkin, I. P. Shestakov, “In memory of Valeriy Matveevich Kopytov”, Algebra Logika, 61:6 (2022),  I–IV  mathnet
1993
40. V. G. Bardakov, “To the theory of braid groups”, Sibirsk. Mat. Zh., 34:2 (1993),  220–221  mathnet  zmath

Presentations in Math-Net.Ru
1. Произведение квандловых структур
V. G. Bardakov

November 11, 2022 15:00
2. Виртуальные узлы и косы
V. G. Bardakov

August 12, 2021 14:30
3. Cимплициальные структуры на группах виртуальных крашеных кос
V. G. Bardakov
December readings in Tomsk
December 15, 2018 09:30
4. On representations of virtual braid group and groups of virtual links
V. G. Bardakov
III International Conference "Quantum Topology"
June 24, 2016 16:20   

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