• 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.

• 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 the Korean Mathematical Society
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• v.50 no.4
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• pp.813-828
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• 2013

It is known that generalized free products of finitely generated nilpotent groups are conjugacy separable when the amalgamated subgroups are cyclic or central in both factor groups. However, those generalized free products may not be conjugacy separable when the amalgamated subgroup is a direct product of two infinite cycles. In this paper we show that generalized free products of finitely generated nilpotent groups are conjugacy separable when the amalgamated subgroup is ${\langle}h{\rangle}{\times}D$, where D is in the center of both factors.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.265-281
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• 2021

In the kneading theory developed by Milnor and Thurston, it is proved that the kneading matrix and the kneading determinant associated with a continuous piecewise monotone map are invariant under orientation-preserving conjugacy. This paper considers the problem for orientation-reversing conjugacy and proves that the former is not an invariant while the latter is. It also presents applications of the result towards the computational complexity of kneading matrices and the classification of maps up to topological conjugacy.

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.109-119
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• 2022

In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We compare the new notion of conjugacy with existing notions, characterize the conjugacy in subsemigroups of partial transformations through digraphs and restrictive partial homomorphisms.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.307-313
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• 2023

In this paper, we study the n-dimensional Möbius transformation. We obtain several conjugacy invariants and give a conjugacy classification for n-dimensional Möbius transformation.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1195-1204
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• 2010

In this paper, we prove a criterion of conjugacy separability of generalized free products of polycyclic-by-finite groups with a non cyclic amalgamated subgroup. Applying this criterion, we prove that certain generalized free products of polycyclic-by-finite groups are conjugacy separable.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.161-175
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• 1997

We classify free actions of finite abelian groups on the 3-dimensional nilmanifold, up to topological conjugacy. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal subgroups of almost Bieberbach groups of finite index, up to affine conjugacy.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.719-726
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• 1998

In this paper, we consider conjugacy of subgroups of some split metacyclic groups of odd prime power order to determine the numbers of conjugacy classes of subgroups of those groups. The study was motivated by the linear isomorphism problem of metacyclic primitive linear groups.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1319-1327
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• 2020

In this paper, we find new conjugacy invariants of Sl(3, ℍ). This result is a generalization of Foreman's result for Sl(2, ℍ).