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Сиб. электрон. матем. изв., 2023, том 20, выпуск 1, страницы 293–305 (Mi semr1588)

Undecidability of the submonoid membership problem for a sufficiently large finite direct power of the Heisenberg group
V. A. Roman'kov

Список литературы

1. F. Bassino, I. Kapovich, M. Lohrey, A. Miasnikov, C. Nicaud, A. Nikolaev, I. Rivin, V. Shpilrain, A. Ushakov, P. Weil, Complexity and randomness in group theory, GAGTA book, 1, de Gruyter, Berlin, 2020  mathscinet  zmath
2. 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, Germany, 2019, 44  mathscinet  zmath
3. S.-Ki Ko, R. Niskanen, R. Niskanen, I. Potapov, “On the identity problem for the special linear group and the Heisenberg group”, 45th international colloquium on automata, languages, and programming. ICALP 2018, Proceedings (Prague, Czech Republic, July 9-13, 2018), LIPIcs - Leibniz Int. Proc. Inform., 107, eds. Chatzigiannakis Ioannis et al., 2018, 132  mathscinet  zmath
4. M. Lohrey, “The rational subset membership problem for groups: a survey”, Groups St Andrews 2013, Selected papers of the conference (St. Andrews, UK, August 3-11, 2013), London Mathematical Society Lecture Note Series, 422, eds. Campbell C.M. et al., Cambridge University Press, Cambridge, 2015, 368–389  mathscinet  zmath
5. A.I. Maltsev, “On homomorphisms onto finite groups”, Transl., Ser. 2, Am. Math. Soc., 119 (1983), 67–79  zmath
6. Yu.V. Matiyasevich, “Enumerable sets are diophantine”, Sov. Math., Dokl., 11:2 (1970), 354–357  mathscinet  zmath
7. Yu.V. Matiyasevich, “A Diophantine representation of enumerable predicates”, Izv. Akad. Nauk SSSR, Ser. Mat., 35 (1971), 3–30  mathnet  mathscinet  zmath
8. Yu. Matiyasevich, “Some purely mathematical results inspired by mathematical logic”, Proc. Fifth Intern. Congr. Logic, Methodology and Philos. of Sci. (London, Ont., 1995), 1977, 121–127  mathscinet  zmath
9. Y. Matijasevic, J. Robinson, “Reduction of an arbitrary diophantine equation to one in 13 unknowns”, Acta Arith., 27 (1975), 521–553  crossref  mathscinet  zmath
10. G.A. Noskov, V.N. Remeslennikov, V.A. Roman'kov, “Infinite groups”, J. Sov. Math., 18:5 (1982), 669–735  mathnet  crossref  zmath
11. 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
12. V.A. Roman'kov, “Algorithmic theory of solvable groups”, Prikl. Diskr. Mat., 52 (2021), 16–64  mathnet  mathscinet  zmath
13. V.A. Roman'kov, “Two problems for solvable and nilpotent groups”, Algebra Logic, 59:6 (2021), 483–492  mathnet  crossref  mathscinet  zmath
14. V.A, Roman'kov, “Positive elements and sufficient conditions for solvability of the submonoid membership problem for nilpotent groups of class two”, Sib. Èlectron. Mat. Izv., 19:1 (2022), 387–403  mathnet  mathscinet  zmath
15. V.A. Roman'kov, “Unsolvability of the submonoid membership problem for a free nilpotent group of class $l\geq 2$ of a sufficiently large rank”, Izvestiya Math. (to appear)  mathscinet
16. T. Skolem, Diophantische Gleichungen, Springer, Berlin, 1938  zmath


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