ON ONE PROBLEM OF OCCURRENCE IN SOME ARTIN STRUCTURES
Irina Vasil’evna Dobrynina, Evgeny V. Manokhin · SOFT MEASUREMENTS AND COMPUTING · 2024
The problem of entering a subgroup is algorithmic, and its solution causes great difficulties in various classes of groups. The same applies to group structures. In this paper, the authors consider the solution of a special case of the general problem of occurrence in the socalled Artin structures. They have the structure of a tree, at the vertices of which there are Artin groups that have an extralarge or woody appearance. Previously, the problem of entering a subgroup generated by a single element was studied for such structures. The authors use methods based on a geometric approach based on the study of diagrams. A special case of the problem of entry is the entry into the socalled parabolic subgroup, that is, a subgroup in which some of the forming elements of the group are removed. The proposed methods make it possible to solve this problem more simply. The solution of the problem considered in the article in Artin groups has not been generally obtained.