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ЖУРНАЛЫ // Сибирские электронные математические известия

Сиб. электрон. матем. изв., 2022, том 19, выпуск 1, страницы 387–403 (Mi semr1510)

Positive elements and sufficient conditions for solvability of the submonoid membership problem for nilpotent groups of class two
V. A. Roman'kov

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  mathscinet  zmath
2. S.I. Adian, “Unsolvability of some algorithmic problems in the theory of groups”, Tr. Mosk. Mat. Obshch., 6, 1957, 231–298  mathnet  mathscinet  zmath
3. S.I. Adian, V.G. Durnev, “Decision problems for groups and semigroups”, Russ. Math. Surv., 55:2 (2000), 207–296  mathnet  crossref  mathscinet  zmath
4. V. Diekert, O. Kharlampovich, M. Lohrey, A. Myasnikov, “Algorithmic problems in group theory (Dagstuhl Seminar 19131)”, Dagstuhl Reports, 9:3 (2019), 83–110  mathscinet
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  mathscinet  zmath
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  crossref  mathscinet  zmath
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  crossref  mathscinet  zmath
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  crossref  mathscinet  zmath
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  crossref  mathscinet  zmath
10. M. Benois, “Parties rationnelles du groupe libre”, C. R. Acad. Sci. Paris, Sér. A, 269 (1969), 1188–1190  mathscinet  zmath
11. S.P. Boyd, L. Vandenberghe, Convex optimization, Cambridge University Press, Cambridge, 2004  mathscinet  zmath
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  mathscinet
13. S. Eilenberg, M.P. Schützenberger, “Rational sets in commutative monoids”, J. Algebra, 13 (1969), 173–191  crossref  mathscinet  zmath
14. E. Formanek, “Conjugacy separability in polycyclic groups”, J. Algebra, 42:1 (1976), 1–10  crossref  mathscinet  zmath
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  crossref  mathscinet  zmath
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  crossref  mathscinet  zmath
17. F. Grunewald, D. Segal, “Some general algorithms. I: Arithmetic groups”, Ann. Math. (2), 112:3 (1980), 531–583  crossref  mathscinet  zmath; “Some general algorithms. II: Nilpotent groups”, 585–617  zmath
18. Z. Grunschlag, Algorithms in geometric group theory, PhD thesis, University of California, Berkley, 1999  mathscinet
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  mathscinet  zmath
20. M. Hall jun., The theory of groups, The Macmillan Company, New York, 1959  mathscinet  zmath
21. O.G. Harlampovich, “A finitely presented solvable group with undecidable word problem”, Math. USSR-Izvestiya, 19:1 (1982), 151–169  mathnet  crossref  mathscinet  adsnasa
22. R. Lipton, Y. Zalstein, “Word problems solvable in logspace”, J. Assoc. Comput. Math., 24 (1977), 522–526  crossref  mathscinet  zmath
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  mathscinet  zmath
24. M. Lohrey, B. Steinberg, “Tilings and submonoids of metabelian groups”, Theory Comput. Syst., 48:2 (2011), 411–427  crossref  mathscinet  zmath  elib
25. J. Macdonald, A. Myasnikov, A. Nikolaev, S. Vassileva, Logspace and compressed-word computations in nilpotent groups, arXiv: 1503.03888v3  mathscinet
26. J. Macdonald, A. Miasnikov, D. Ovchinnikov, “Low-complexity computations for nilpotent subgroup problems”, Int. J. Algebra Comput., 29:4 (2019), 639–661  crossref  mathscinet  zmath
27. Y. Matijasevic, J. Robinson, “Reduction of an arbitrary diophantine equation to one in 13 unknowns”, Acta Arith., 27 (1975), 521–553  crossref  mathscinet  zmath
28. Ch.F. III Miller, “Decision problems in algebraic classes of groups (a survey)”, Studies Logic Foundations Math., 71 (1973), 507–523  crossref  mathscinet  zmath
29. A. Myasnikov, V. Roman'kov, “On rationality of verbal subsets in a group”, Theory Comput. Syst., 52:4 (2013), 587–598  crossref  mathscinet  zmath  elib
30. A. Myasnikov, V. Shpilrain, A. Ushakov, Group-based cryptography, Advanced Courses in Mathematics, CRM, Barcelona; Birkhäuser, 2008  mathscinet  zmath
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  crossref  mathscinet  zmath
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  mathscinet  zmath
35. G.A. Noskov, “Conjugacy problem in metabelian groups”, Math. Notes, 31:4 (1982), 252–258  mathnet  crossref  mathscinet  zmath
36. G.A. Noskov, V.N. Remeslennikov, V.A. Roman'kov, “Infinite groups”, J. Sov. Math., 18:5 (1982), 669–735  mathnet  crossref  zmath
37. P.S. Novikov, “On the algorithmic unsolbability of the word problem”, Dokl. Akad. Nauk SSSR, 85:4 (1952), 709–712  mathscinet  zmath
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  mathnet  mathscinet  zmath
39. M.O. Rabin, “Recursive unsolvability of group theoretic problems”, Ann. Math. (2), 67 (1958), 172–194  crossref  mathscinet  zmath
40. V.N. Remeslennikov, “Conjugacy in polycyclic groups”, Algebra Logic, 8 (1971), 404–411  mathnet  crossref  mathscinet  zmath
41. V.N. Remeslennikov, V.A. Roman'kov, “Model-theoretic and algorithmic questions in group theory”, J. Sov. Math., 31:3 (1985), 2887–2939  mathnet  crossref  mathscinet  zmath
42. N.S. Romanovskii, “Some algorithmic problems for solvable groups”, Algebra Logika, 13:1 (1974), 26–34  mathnet  crossref  mathscinet  zmath
43. N.S. Romanovskii, “The occurrence problem for extensions of abelian groups by nilpotent groups”, Sib. Math. J., 21 (1980), 273–276  mathnet  crossref  mathscinet  zmath
44. V.A. Roman'kov, “Automorphisms of groups”, Acta Appl. Math., 29:3 (1992), 241–280  crossref  mathscinet  zmath
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  crossref  mathscinet  zmath
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  mathnet  crossref  mathscinet  zmath
52. V.A. Roman'kov, “Algorithmic theory of solvable groups”, Prikl. Diskr. Mat., 52 (2021), 16–64  mathnet  mathscinet  zmath
53. R.A. Sarkisjan, “Algorithmic questions for linear algebraic groups, I”, Math. USSR, Sb., 41:2 (1982), 149–189  crossref  mathscinet  zmath
54. R.A. Sarkisjan, “Algorithmic questions for linear algebraic groups, II”, Math. USSR, Sb., 41:3 (1982), 329–359  mathnet  crossref  mathscinet  zmath
55. D. Segal, “Decidable properties of polycyclic groups”, Proc. Lond. Math. Soc., III. Ser., 61:3 (1990), 497–528  crossref  mathscinet  zmath
56. E.I. Timoshenko, “Algorithmic problems for metabelian groups”, Algebra and Logic, 12:2 (1973), 132–137  crossref  mathscinet
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


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