• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.495-502
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• 2008

We show that free products of finitely generated and residually p-finite nilpotent groups, amalgamating p-closed central subgroups are residually p-finite. As a consequence, we are able to show that generalized free products of residually p-finite abelian groups are residually p-finite if the amalgamated subgroup is closed in the pro-p topology on each of the factors.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1741-1752
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• 2008

Grossman [7] showed that certain cyclically pinched 1-relator groups have residually finite outer automorphism groups. In this paper we prove that tree products of finitely generated free groups amalgamating maximal cyclic subgroups have residually finite outer automorphism groups. We also prove that polygonal products of finitely generated central subgroup separable groups amalgamating trivial intersecting central subgroups have residually finite outer automorphism groups.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.461-466
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• 2016

In general, polygonal products of free groups are not residually finite. Using the residual finiteness of polygonal products of nilpotent groups, we show that certain polygonal products of free groups are residually finite.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.785-796
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• 2024

Let p be a prime. A group G is said to be residually p-finite if for each non-trivial element x of G, there exists a normal subgroup N of index a power of p in G such that x is not in N. In this note we shall prove that certain HNN extensions of free abelian groups of finite rank are residually p-finite. In addition some of these HNN extensions are subgroup separable. Characterisations for certain one-relator groups and similar groups including the Baumslag-Solitar groups to be residually p-finite are proved.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.45-52
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• 2008

We show that certain polygonal products of any four groups, amalgamating central subgroups with trivial intersections, have Property E. Using this result, we derive that outer automorphism groups of polygonal products of four polycyclic-by-finite groups, amalgamating central subgroups with trivial intersections, are residually finite.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.603-612
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• 2021

We generalize 3-manifolds supporting non-positively curved metric to construct manifolds which have the following properties : (1) They are not locally CAT(0). (2) Their fundamental groups are residually finite. (3) They have subgroup separability for some abelian subgroups.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.367-374
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• 2003

Let N be a Closed n-manifold with residually finite, torsion free $\pi$$_1$(N) and finite H$_1$,(N). Suppose that $\pi$$\_$k/(N)=0 for 1 < k < n-1. We show that N is a codimension-n PL fibrator if and only if N does not cover itself regularly and cyclically up to homotopy type, provided $\pi$$_1$(N) satisfies a certain condition.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1033-1041
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• 2016

We show that, for any non-zero integers ${\lambda}$, ${\mu}$, ${\nu}$, ${\xi}$, class-preserving automorphisms of the group $$G({\lambda},{\mu},{\nu},{\xi})={\langle}a,b,t:b^{-1}a^{\lambda}b=a^{\mu},t^{-1}a^{\nu}t=b^{\xi}{\rangle}$$ are all inner. Hence, by using Grossman's result, the outer automorphism group of $G({\lambda},{\pm}{\lambda},{\nu},{\xi})$ is residually finite.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.61-71
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• 2007

A group G is called cyclic subgroup separable for the cyclic subgroup H if for each $x\;{\in}\;G{\backslash}H$, there exists a normal subgroup N of finite index in G such that $x\;{\not\in}\;HN$. Clearly a cyclic subgroup separable group is residually finite. In this note we show that certain polygonal products of cyclic subgroup separable groups amalgamating normal subgroups are again cyclic subgroup separable. We then apply our results to polygonal products of polycyclic-by-finite groups and free-by-finite groups.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.555-561
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• 2005

In this note we give characterizations for certain HNN extensions with central associated subgroups to be residually finite. We then apply our results to HNN extensions of polycyclic-by-finite groups.