부산대학교 도서관

In this note, we study cyclic conjugacy separability and conjugacy separability of generalized free products. We first prove the enterions for generalized free products to be cyclic conjugacy separable and conjugacy separable. Our method involved a concept first introduced by G. Baumslag, called filterations. This method makes our criterions clearer and easier for applications. We then extend our criterions to generalized free products of polycyclic-by-finite groups or surface groups amalgamating a central subgroup. Finally, we show that generalized free products of free groups or finitely generated torsion-free nilpotent groups amalgamating an infinite cyclic subgroup are both cyclic conjugacy separable and conjugacy separable. [ABSTRACT FROM AUTHOR]