http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
THE RESIDUAL FINITENESS OF CERTAIN HNN EXTENSIONS
Choon, Wong-Peng,Bin, Wong-Kok Korean Mathematical Society 2005 대한수학회보 Vol.42 No.3
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.
The residual finiteness of certain HNN extensions
Wong Peng Choon,Wong Kok Bin 대한수학회 2005 대한수학회보 Vol.42 No.3
In this note we give characterizations for certain HNNextensions with central associated subgroups to be residually nite.We then apply our results to HNN extensions of polycyclic-by-finite groups.
POLYGONAL PRODUCTS OF RESIDUALLY FINITE GROUPS
Wong, Kok-Bin,Wong, Peng-Choon Korean Mathematical Society 2007 대한수학회보 Vol.44 No.1
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.
CYCLIC SUBGROUP SEPARABILITY OF CERTAIN GRAPH PRODUCTS OF SUBGROUP SEPARABLE GROUPS
Wong, Kok Bin,Wong, Peng Choon Korean Mathematical Society 2013 대한수학회보 Vol.50 No.5
In this paper, we show that tree products of certain subgroup separable groups amalgamating normal subgroups are cyclic subgroup separable. We then extend this result to certain graph product of certain subgroup separable groups amalgamating normal subgroups, that is we show that if the graph has exactly one cycle and the cycle is of length at least four, then the graph product is cyclic subgroup separable.
Cyclic subgroup separability of certain graph products of subgroup separable groups
Kok Bin Wong,Peng Choon Wong 대한수학회 2013 대한수학회보 Vol.50 No.5
In this paper, we show that tree products ofcertain subgroup separable groups amalgamating normal subgroups are cyclic subgroup separable. We then extend this result to certain graph product of certain subgroup separable groups amalgamating normal subgroups, that is we show that if the graph has exactly one cycle and the cycle is of length at least four, then the graph product is cyclic subgroup separable.
Residual $p$-finiteness of certain HNN extensions of free abelian groups of finite rank
Chiew Khiam Tang,Peng Choon Wong 대한수학회 2024 대한수학회보 Vol.61 No.3
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.
WEAK POTENCY AND CYCLIC SUBGROUP SEPARABILITY OF CERTAIN FREE PRODUCTS AND TREE PRODUCTS
Muhammad Sufi Mohd Asri,Wan Ainun Mior Othman,Kok Bin Wong,Peng Choon Wong 대한수학회 2023 대한수학회보 Vol.60 No.5
In this note, we shall show that the generalized free products of subgroup separable groups amalgamating a subgroup which itself is a finite extension of a finitely generated normal subgroup of both the factor groups are weakly potent and cyclic subgroup separable. Then we apply our result to generalized free products of finite extensions of finitely generated torsion-free nilpotent groups. Finally, we shall show that their tree products are cyclic subgroup separable.