On the solvability of the occurrence problem in a certain class of Artin groups
https://doi.org/10.22405/2226-8383-2023-24-1-213-218
Abstract
The paper solves the problem of entering into the Artin group with a woody structure.
About the Authors
Vladimir Nikolaevich BezverkhniiRussian Federation
doctor of physical and mathematical sciences, professor
Natalia Borisovna Bezverkhnyaya
Russian Federation
candidate of physical and mathematical sciences
References
1. Novikov P. S., 1955, “On algorithmic unsolvability of the word identity problem in group theory”.
2. // Proceedings of the MIAN USSR, 44. pp. 1–144.
3. Appel K., Schupp P., 1983, “Artin groups and infinite Coxeter groups” // Ivent. Math., Vd 72,
4. pp. 201–220.
5. Appel K., 1984, “One Artin groups and Coxeter groups of large type” // Contemp. Math., V.33,
6. pp. 50–78.
7. Bezverkhny. V. N., 1986, “Solution of the word conjugacy problem in Artin and Coxeter
8. groups of large type” // Algorithmic problems of the theory of groups and semigroups. Inter.
9. universities. collection of scientific tr. Tula, pp. 26–61.
10. Bezverkhny. V. N., 2003, “On Artin and Coxeter groups with a woody structure” // Algebra
11. and number theory. Theses V international. conf. Tula, pp. 33–34.
12. Bezverkhny V. N. Karpova O. Yu., 2006, “The problem of equality and conjugacy of words in
13. Artin groups with a tree structure” // News of TulSU. Ser. Mathematics. Mechanics. Computer
14. science., Vol.12, Iss. 1, pp. 67–82.
15. Bezverkhny V. N., Bezverkhny N. B., 2019, Solving the problem of equality and conjugacy of
16. words in a certain class of Artin groups. // Fundamental and Applied Mathematics, vol. 22, No.
17. , pp. 9–27.
18. Lyndon R., Shupp P., 1980, “Combinatorial theory of groups” // M. Mir.
19. Bezverkhny. V.N., 1999, “Solution of the problem of generalized conjugacy of words in Artin
20. groups of large type” // Fundamental and Applied Mathematics, Vol. 5, Iss. 1, pp. 1–38.
21. Bezverkhny V.N., 1985, “The unsolvability of the problem of occurrence in Artin groups of finite
22. type” // Sib. Mat. zhur. TXXVI. № 5, pp. 27–42.
23. Makanina T.A., 1981, “The problem of occurrence for groups of braids 𝐵(𝑛 + 1) at 𝑛 + 1 ⩾ 5”
24. //Math. notes, Vol. 29, № 1. pp. 31–33.
25. Bezverkhny V.N., ,1986 “Solution of the problem of occurrence in some classes of groups with one
26. defining relation” // Algorithmic problems of the theory of groups and semigroups. Intercollegiate
27. collection of scientific papers. Tula, pp. 3–21.
28. Bezverkhny V.N., 1981, “Solution of the problem of occurrence in the class of HNN-groups”
29. //Algorithmic problems of the theory of groups and semigroups. Intercollegiate collection of
30. scientific papers. Tula, pp. 20–62.
31. Bezverkhny V.N., 1972, “The solution of the problem of occurrence for one class of groups”
32. //Questions of the theory of groups and semigroups. Tula, TSPI. pp. 3–86.
Review
For citations:
Bezverkhnii V.N., Bezverkhnyaya N.B. On the solvability of the occurrence problem in a certain class of Artin groups. Chebyshevskii Sbornik. 2023;24(1):213-218. (In Russ.) https://doi.org/10.22405/2226-8383-2023-24-1-213-218