The isomorphism problem for a class of finitely generated metabelian groups

Key Points

• To develop an algorithm for determining if two finitely generated metabelian groups are isomorphic.
• Created an algorithm for isomorphism testing of finitely generated metabelian groups.
• Focused on groups associated with non-constant integer polynomials.
• Utilized concepts of finite torsion-free rank in the analysis.
• The algorithm can effectively decide the isomorphism of the groups.
• It associates each non-constant integer polynomial with a unique metabelian group.
• Demonstrated significant progress in solving the isomorphism problem for this class of groups.