POLYGONAL PRODUCTS OF RESIDUALLY FINITE GROUPS

Title & Authors
POLYGONAL PRODUCTS OF RESIDUALLY FINITE GROUPS
Wong, Kok-Bin; Wong, Peng-Choon;

Abstract
A group G is called cyclic subgroup separable for the cyclic subgroup H if for each $\small{x\;{\in}\;G{\backslash}H}$, there exists a normal subgroup N of finite index in G such that $\small{x\;{\not\in}\;HN}$. 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.
Keywords
subgroup separable;polygonal products;polycyclic-by-finite groups;free-by-finite groups;abelian groups;
Language
English
Cited by
1.
CYCLIC SUBGROUP SEPARABILITY OF CERTAIN GRAPH PRODUCTS OF SUBGROUP SEPARABLE GROUPS,;;

대한수학회보, 2013. vol.50. 5, pp.1753-1763
1.
The Weakly Potency of Certain HNN Extensions of Nilpotent Groups, Algebra Colloquium, 2014, 21, 04, 689
2.
CYCLIC SUBGROUP SEPARABILITY OF CERTAIN GRAPH PRODUCTS OF SUBGROUP SEPARABLE GROUPS, Bulletin of the Korean Mathematical Society, 2013, 50, 5, 1753
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