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On the occurrence problem in some classes of Artin groups

https://doi.org/10.22405/2226-8383-2025-26-4-240-256

Abstract

In this article, the occurrence problem in Artin groups with arboreal is solved.

About the Authors

Vladimir Nikolaevich Bezverkhnii
Russian Customs Academy
Russian Federation

doctor of physical and mathematical sciences



Nataliya Borisovna Bezverhnaya
MTUCI
Russian Federation

candidate of physical and mathematical sciences



Andrey Sergeevich Ugarov
Tula State Lev Tolstoy Pedagogical University
Russian Federation


References

1. Markov A.A., 1945, “Fundamentals of algebraic braid theory”, Trudy Matematicheskogo Instituta imeni V.A. Steklova, Vol 6, pp 1–54.

2. Garside F.A., 1969, “The braid group and other groups”, Quarterly Journal of Mathematics, Vol 20, no 2, pp 235–254.

3. Brieskorn E., Saito K., 1974, “Artin groups and Coxeter groups”, Mathematics, Vol 18, no 6, pp 56–79.

4. Bezverkhny V.N., 1985, “The unsolvability of the problem of occurrence in Artin groups of finite type”, Sibirskii Matematicheskii Zhurnal, Vol 26, no 5, pp 27–42.

5. Appel K., Schupp P., 1983, “Artin groups and infinite Coxeter groups”, Inventiones Mathematicae, Vol 72, no 2, pp 201–220.

6. Appel K., 1984, “One Artin groups and infinite Coxeter groups”, Contemporary Mathematics, Vol 33, pp 50–78.

7. Bezverkhny V.N., 1986, “Solving the problem of conjugation of words in the Artin and Coxeter groups of a large type”, Algorithmic Problems of Group and Semigroup Theory, pp 26–61.

8. Bezverkhny V.N., 1999, “Solution of the problem of generalized conjugation of words in largetype Artin groups”, Fundamental and Applied Mathematics, Vol 5, no 1, pp 1–38.

9. Bezverkhny V.N., 2003, “On Artin and Coxeter groups with a woody structure”, V International Conference on Algebra and Number Theory, pp 33–34.

10. Bezverkhny V.N., Karpova O.Yu., 2006, “The problem of equality and conjugacy in groups of wood with a woody structure”, Izvestiya Tulskogo Gosudarstvennogo Universiteta, Vol 12, pp 67–82.

11. Bezverkhny V.N., 2014, “Solving the problem of equality and conjugation of words in some classes of Artin and Coxeter groups”, XII International Conference on Algebra and Number Theory, p 6.

12. Bezverkhnii V.N., Bezverkhnyaya N.B., 2021, “Solution of the problem of equality and conjugacy of word in certain class of Artin groups”, Journal of Mathematical Science, Vol 257, pp 751–764.

13. Bezverkhny V.N., 1974, “On the intersection of finitely generated subgroups of free groups”, Collection of Scientific Papers, Vol 2, pp 51–56.

14. Bezverkhny V.N., Rollov E.V., 1974, “On subgroups of a free product of groups”, Modern Algebra, pp 16–31.

15. Bezverkhny V.N., 1998, “On the intersection of subgroups in HNN groups”, Fundamental and Applied Mathematics, Vol 4, pp 199–222.

16. Bezverhnaya I.S., 1981, “On the conjugacy of finite sets of subgroups in the free production of groups”, Algorithmic Problems of Group and Semigroup Theory, pp 103–116.

17. Bezverkhny V.N., 1972, “Solution of the problem of occurrence for one class of groups”, Questions of Group and Semigroup Theory, pp 3–86.

18. Bezverkhny V.N., 1981, “The solution of the problem of entry into the class of HNN groups”, Algorithmic Problems of Group and Semigroup Theory, pp 20–62.

19. Bezverkhny V.N., 1986, “Solution of the problem of occurrence in some classes of groups with one defining ratio”, Algorithmic Problems of Group and Semigroup Theory, pp 3–21.

20. Bezverkhny V.N., 1985, “Solution of the problem of occurrence in some classes of groups with one defining relation with a nontrivial center”, Sibirskii Matematicheskii Zhurnal, Vol 26, no 2, pp 219–220.

21. Dobrynina I.V., 2022, “On subgroups in Artin groups with tree structure”, Chebyshevskii Sbornik, Vol 23, no 3, pp 118–132.


Review

For citations:


Bezverkhnii V.N., Bezverhnaya N.B., Ugarov A.S. On the occurrence problem in some classes of Artin groups. Chebyshevskii Sbornik. 2025;26(4):240-256. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-4-240-256

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