|
|
|
Список литературы
|
|
|
1. |
S.I. Adian, “Algorithmic unsolvability of problems of recognition of certain properties of groups”, Dokl. Akad. Nauk SSSR, 103:4 (1955), 533–535 |
2. |
S.I. Adian, “Unsolvability of some algorithmic problems in the theory of groups”, Tr. Mosk. Mat. Obshch., 6, 1957, 231–298 |
3. |
S.I. Adian, V.G. Durnev, “Decision problems for groups and semigroups”, Russ. Math. Surv., 55:2 (2000), 207–296 |
4. |
V. Diekert, O. Kharlampovich, M. Lohrey, A. Myasnikov, “Algorithmic problems in group theory (Dagstuhl Seminar 19131)”, Dagstuhl Reports, 9:3 (2019), 83–110 |
5. |
F. Bassino, I. Kapovich, M. Lohrey, A. Miasnikov, C. Nicaud, A. Nikolaev, I. Rivin, Complexity and randomness in group theory, GAGTA, 1, eds. A. Ushakov, P. Weil,, de Gruyter, Berlin, 2020 |
6. |
G. Baumslag, F.B. Cannonito, D.J.S. Robinson, “The algorithmic theory of finitely generated metabelian groups”, Trans. Am. Math. Soc., 344:2 (1994), 629–648 |
7. |
G. Baumslag, F.B. Cannonito, D.J.S. Robinson, D. Segal, “The algorithmic theory of polycyclic-by-finite groups”, J. Algebra, 141:1 (1991), 118–149 |
8. |
G. Baumslag, D. Gildenhuys, R. Strebel, “Algorithmically insoluble problems about finitely presented solvable groups, Lie and associative algebras. I”, J. Pure Appl. Algebra, 39 (1986), 53–94 |
9. |
G. Baumslag, D. Gildenhuys, R. Strebel, “Algorithmically insoluble problems about finitely presented solvable groups, Lie and associative algebras. II”, J. Algebra, 97 (1985), 278–285 |
10. |
M. Benois, “Parties rationnelles du groupe libre”, C. R. Acad. Sci. Paris, Sér. A, 269 (1969), 1188–1190 |
11. |
S.P. Boyd, L. Vandenberghe, Convex optimization, Cambridge University Press, Cambridge, 2004 |
12. |
T. Colcombet, J. Ouaknine, P. Semukhin, J. Worrell, “On reachability problems for low dimensional matrix semigroups”, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019), LIPIcs, 132, eds. C. Baier et al., Schloss Dagstuhl – Leibniz-Zentrum f$\ddot{\rm u}$r Informatik, Dagstuhl, 2019, 44:1–44:15 |
13. |
S. Eilenberg, M.P. Schützenberger, “Rational sets in commutative monoids”, J. Algebra, 13 (1969), 173–191 |
14. |
E. Formanek, “Conjugacy separability in polycyclic groups”, J. Algebra, 42:1 (1976), 1–10 |
15. |
R.H. Gilman, “Formal languages and infinite groups”, Geometric and computational perspectives on infinite groups, Proceedings of a joint DIMACS/Geometry Center workshop (January 3–14, 1994, the University of Minnesota, Minneapolis, MN, USA and March 17-20, 1994, Princeton, NJ, USA), DIMACS, Ser. Discrete Math. Theor. Comput. Sci., 25, eds. Baumslag G. et al., AMS, Providence, 1996, 27–51 |
16. |
F. Grunewald, D. Segal, “The solubility of certain decision problems in arithmetic and algebra”, Bull. Am. Math. Soc., New Ser., 1:6 (1979), 915–918 |
17. |
F. Grunewald, D. Segal, “Some general algorithms. I: Arithmetic groups”, Ann. Math. (2), 112:3 (1980), 531–583 ; “Some general algorithms. II: Nilpotent groups”, 585–617 |
18. |
Z. Grunschlag, Algorithms in geometric group theory, PhD thesis, University of California, Berkley, 1999 |
19. |
P. Hall, Nilpotent groups, Notes of lectures given at the Canadian Mathematical Congress, summer seminar (University of Alberta, Edmonton, 12-30 August 1957), Queen Mary College (University of London), London, 1969 |
20. |
M. Hall jun., The theory of groups, The Macmillan Company, New York, 1959 |
21. |
O.G. Harlampovich, “A finitely presented solvable group with undecidable word problem”, Math. USSR-Izvestiya, 19:1 (1982), 151–169 |
22. |
R. Lipton, Y. Zalstein, “Word problems solvable in logspace”, J. Assoc. Comput. Math., 24 (1977), 522–526 |
23. |
M. Lohrey, “The rational subset membership problem for groups: a survey”, Groups St Andrews 2013, Selected papers of the conference, London Mathematical Society Lecture Note Series, 422, eds. Campbell C.M. et al., Cambridge University Press, 2015, 368–389 |
24. |
M. Lohrey, B. Steinberg, “Tilings and submonoids of metabelian groups”, Theory Comput. Syst., 48:2 (2011), 411–427 |
25. |
J. Macdonald, A. Myasnikov, A. Nikolaev, S. Vassileva, Logspace and compressed-word computations in nilpotent groups, arXiv: 1503.03888v3 |
26. |
J. Macdonald, A. Miasnikov, D. Ovchinnikov, “Low-complexity computations for nilpotent subgroup problems”, Int. J. Algebra Comput., 29:4 (2019), 639–661 |
27. |
Y. Matijasevic, J. Robinson, “Reduction of an arbitrary diophantine equation to one in 13 unknowns”, Acta Arith., 27 (1975), 521–553 |
28. |
Ch.F. III Miller, “Decision problems in algebraic classes of groups (a survey)”, Studies Logic Foundations Math., 71 (1973), 507–523 |
29. |
A. Myasnikov, V. Roman'kov, “On rationality of verbal subsets in a group”, Theory Comput. Syst., 52:4 (2013), 587–598 |
30. |
A. Myasnikov, V. Shpilrain, A. Ushakov, Group-based cryptography, Advanced Courses in Mathematics, CRM, Barcelona; Birkhäuser, 2008 |
31. |
A. Myasnikov, V. Shpilrain, A. Ushakov, Non-commutative cryptography and complexity of group-theoretic problems, Mathematical Surveys and Monographs, 177, Amer. Math. Soc., Providence, 2011 |
32. |
M.Yu. Nedbay, “The rational subset membership problem for finitely generated abelian groups”, Vestnik Omskogo universiteta, 1999:3 (1999), 37–41 |
33. |
M.Yu. Nedbay, “The rational subset membership problem for free products of groups”, Vestnik Omskogo universiteta, 2000:2 (2000), 17–18 |
34. |
M. Newman, Integral matrices, Pure and Applied Mathematics, 45, Academic Press, New York-London, 1972 |
35. |
G.A. Noskov, “Conjugacy problem in metabelian groups”, Math. Notes, 31:4 (1982), 252–258 |
36. |
G.A. Noskov, V.N. Remeslennikov, V.A. Roman'kov, “Infinite groups”, J. Sov. Math., 18:5 (1982), 669–735 |
37. |
P.S. Novikov, “On the algorithmic unsolbability of the word problem”, Dokl. Akad. Nauk SSSR, 85:4 (1952), 709–712 |
38. |
P.S. Novikov, “On the algorithmic unsolvability of the word problem in group theory”, Tr. Mat. Inst. Steklova, 44, Acad. Sci. USSR, M., 1955 |
39. |
M.O. Rabin, “Recursive unsolvability of group theoretic problems”, Ann. Math. (2), 67 (1958), 172–194 |
40. |
V.N. Remeslennikov, “Conjugacy in polycyclic groups”, Algebra Logic, 8 (1971), 404–411 |
41. |
V.N. Remeslennikov, V.A. Roman'kov, “Model-theoretic and algorithmic questions in group theory”, J. Sov. Math., 31:3 (1985), 2887–2939 |
42. |
N.S. Romanovskii, “Some algorithmic problems for solvable groups”, Algebra Logika, 13:1 (1974), 26–34 |
43. |
N.S. Romanovskii, “The occurrence problem for extensions of abelian groups by nilpotent groups”, Sib. Math. J., 21 (1980), 273–276 |
44. |
V.A. Roman'kov, “Automorphisms of groups”, Acta Appl. Math., 29:3 (1992), 241–280 |
45. |
V.A. Roman'kov, “On the occurence problem for rational subsets of a group”, Combinatorial and computing methods in mathematics, Omsk State University, Omsk, 1999, 235–242 |
46. |
V.A. Roman'kov, Rational subsets in groups, Omsk State Univrersity, Omsk, 2014 |
47. |
V.A. Roman'kov, “On algorithmic problems in group theory”, Vestnik Omskogo universiteta, 2017:2(84) (2017), 18–27 |
48. |
V.A. Roman'kov, Essays in algebra and cryptology. Solvable groups, Omsk State University, Omsk, 2017 |
49. |
V.A. Roman'kov, “Polycyclic, metabelian, or soluble of type (FP)$_\infty$ groups with Boolean algebra of rational sets and biautomatic soluble groups are virtually abelian”, Glasg. Math. J., 60:1 (2018), 209–218 |
50. |
V.A. Roman'kov, Algebraic cryptology, OmSU, Omsk, 2020 |
51. |
V.A. Roman'kov, “Two problems for solvable and nilpotent groups”, Algebra Logic, 59:6 (2021), 483–492 |
52. |
V.A. Roman'kov, “Algorithmic theory of solvable groups”, Prikl. Diskr. Mat., 52 (2021), 16–64 |
53. |
R.A. Sarkisjan, “Algorithmic questions for linear algebraic groups, I”, Math. USSR, Sb., 41:2 (1982), 149–189 |
54. |
R.A. Sarkisjan, “Algorithmic questions for linear algebraic groups, II”, Math. USSR, Sb., 41:3 (1982), 329–359 |
55. |
D. Segal, “Decidable properties of polycyclic groups”, Proc. Lond. Math. Soc., III. Ser., 61:3 (1990), 497–528 |
56. |
E.I. Timoshenko, “Algorithmic problems for metabelian groups”, Algebra and Logic, 12:2 (1973), 132–137 |
57. |
O.A. Yurak, “On the simultaneous reduction of elements of abelian groups to positive form”, Vestnik Omskogo universiteta, 2006:3 (2006), 18–19 |
58. |
O.A. Yurak, “On the simultaneous reduction of elements of abelian groups to positive form, II”, Vestnik Omskogo universiteta, 2006:4 (2006), 7–8 |
59. |
O.A. Yurak, “Positive elements of the Heisenberg group”, Vestnik Omskogo universiteta, 2008:2 (2008), 16–19 |