Conjugacy separability and cyclic conjugacy separability of certain HNN extensions, generalised free products and tree products / Lim Hui Min

In this thesis, we study two interrelated strong residually finite properties of groups, namely conjugacy separability and cyclic conjugacy separability. We extend them to certain HNN extensions, generalized free products and tree products where the associated subgroups and amalgamated subgroups are not necessarily cyclic. In the first part of the thesis, we consider HNN extensions. We begin by establishing two criteria, one for conjugacy separability and another for cyclic conjugacy separability. Using these two criteria we establish conditions for HNN extensions where the associated subgroups are central or they are a finite extension of a central subgroup or cyclic to be conjugacy separable and cyclic conjugacy separable. In the second part of the thesis, we consider generalized free products and tree products. We shall consider only cyclic conjugacy separability as results on conjugacy separability are already known. Again we begin by establishing a criterion for cyclic conjugacy separability. We then prove that certain generalized free products and tree products where the amalgamated subgroups are central or they are a finite extension of a central subgroup or cyclic are again cyclic conjugacy separable