On One Algorithm in the Generalized Artin Tree Group

The construction of algorithms and their implementation are one of the important parts of various scientific fields, including combinatorial group theory. In this paper, we consider an algorithm for finding the intersection of subgroups, each of which is generated by one element, in a generalized tree Artin group, which represents the tree product of Artin groups whose graph is a tree, on the one hand, and Artin groups of extra-large type, on the other, with isomorphic subgroups, each from which is generated by some generator of these groups. The results considered in this paper can be used in the further study of Artin groups, in particular, the study their various algorithmic properties, and also contribute to the development of intelligent technologies. Artin groups also find their application in the construction of some cryptosystems, in particular, this applies to the famous braid group, which is part of the class under consideration.