Cyclic subgroup separability of certain graph products of subgroup separable groups
Bull. Korean Math. Soc. 2013 Vol. 50, No. 5, 1753-1763
https://doi.org/10.4134/BKMS.2013.50.5.1753
Published online September 1, 2013
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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