ON AN ALGORITHMIC PROBLEM IN A CERTAIN COXETER GROUP

In this paper, the authors present a geometric algorithm that makes it possible to construct a subgroup equal to the intersection of a pair of singly defined subgroups in a Coxeter group, which is a tree of Coxeter groups, at the vertices of which there are Coxeter groups of extralarge and woody types, and the edges correspond to subgroups generated by some generators of connecting groups. This approach simplifies the solution of algorithmic problems in Coxeter groups. The problem under consideration is of interest from the point of view of studying the combinatorial properties of groups.