Bull. Korean Math. Soc. 2023; 60(5): 1375-1390
Online first article September 6, 2023 Printed September 30, 2023
https://doi.org/10.4134/BKMS.b220715
Copyright © The Korean Mathematical Society.
Muhammad Sufi Mohd Asri, Wan Ainun Mior Othman, Kok Bin Wong, Peng Choon Wong
University of Malaya; University of Malaya; University of Malaya; University of Malaya
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.
Keywords: Generalized free products, tree products, weakly potent, cyclic subgroup separable, residually finite
MSC numbers: Primary 20E06, 20E26, 20F05, 20F10
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2005; 42(3): 555-561
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