Bulletin of the
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BKMS

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Bull. Korean Math. Soc. 2013; 50(5): 1753-1763

Printed September 1, 2013

https://doi.org/10.4134/BKMS.2013.50.5.1753

Copyright © The Korean Mathematical Society.

Cyclic subgroup separability of certain graph products of subgroup separable groups

Kok Bin Wong and Peng Choon Wong

University of Malaya, University of Malaya

Abstract

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.

Keywords: cyclic subgroup separability, graph products, subgroup separable, polycyclic-by-finite groups

MSC numbers: Primary 20E06, 20E26; Secondary 20F10

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