• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.521-530
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• 1997

We first prove a criterion for the conjugacy separability of free products with amalgamation where the amalgamated subgroup is not necessarily cyclic. Applying this result, we show that free products of finite number of polycyclic-by-finite groups with central amalgamation are conjugacy separable. We also show that polygonal products of polycyclic-by-finite groups, amalgamating central cyclic subgroups with trivial intersections, are conjugacy separable.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1237-1256
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• 2023

The tree products of groups with amalgamation subgroups are generalizations of the free products of groups with amalgamation subgroup. The aim of this paper is to construct a tree called the standard tree where the tree products of groups with amalgamation subgroups act without inversions and then find the quotient of this action. Furthermore, we show that if the amalgamation subgroups are finite and the factor groups act on disjoint trees then there exists a tree called the fiber tree where the tree products of groups with amalgamation subgroups act without inversions and find the quotients of this action. If each factor is a tree products with amalgamation subgroups, we get a new fiber tree and the corresponding factors.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.811-827
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• 2000

We find some conditions to derive the conjugacy separability of the free product of conjugacy separable split extensions amalgamated along cyclic retracts. These conditions hold for any double coset separable groups and free-by-cyclic groups with nontrivial center. It was known that free-by-finite, polycyclic-by-finite, and fuchsian groups are double coset separable. Hence free products of those groups amalgamated along cyclic retracts are conjugacy separable.