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On polygonal products of finitely generated abelian groups

Published online by Cambridge University Press:  17 April 2009

Goansu Kim
Goansu Kim
Affiliation:
Department of MathematicsKangnung National UniversityKangnung, Kangwon-Do, 210-702Korea
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Abstract

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We prove that a polygonal product of polycyclic-by-finite groups amalgamating subgroups, with trivial intersections, is cyclic subgroup separable (hence, it is residually finite) if the amalgamated subgroups are contained in the centres of the vertex groups containing them. Hence a polygonal product of finitely generated abelian groups, amalgamating any subgroups with trivial intersections, is cyclic subgroup separable. Unlike this result, most polygonal products of four finitely generated abelian groups, with trivial intersections, are not subgroup separable (LERF). We find necessary and sufficient conditions for certain polygonal products of four groups to be subgroup separable.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 3 , June 1992 , pp. 453 - 462
Copyright
Copyright © Australian Mathematical Society 1992

References

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