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WEAK POTENCY AND CYCLIC SUBGROUP SEPARABILITY OF CERTAIN FREE PRODUCTS AND TREE PRODUCTS
Muhammad Sufi Mohd Asri,Wan Ainun Mior Othman,Kok Bin Wong,Peng Choon Wong 대한수학회 2023 대한수학회보 Vol.60 No.5
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.