On Conjugacy Finite Sets of Subgroups in Some Class of Coxeter Groups

Abstract

The article gives an overview of algorithmic properties of Coxeter groups with tree structure. The paper considers free product of two 2-generated of Coxeter groups amalgamated by cyclic subgroup which refers to Coxeter groups with tree structure. The authors proves decidability of conjugacy problem for finite sets of subgroups in this class of groups.