Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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WEAK POTENCY AND CYCLIC SUBGROUP SEPARABILITY OF CERTAIN FREE PRODUCTS AND TREE PRODUCTS

  • Muhammad Sufi Mohd Asri (Institute of Mathematical Sciences Faculty of Science University of Malaya) ;
  • Wan Ainun Mior Othman (Institute of Mathematical Sciences Faculty of Science University of Malaya) ;
  • Kok Bin Wong (Institute of Mathematical Sciences Faculty of Science University of Malaya) ;
  • Peng Choon Wong (Institute of Mathematical Sciences Faculty of Science University of Malaya)
  • Received : 2022.10.12
  • Accepted : 2023.02.22
  • Published : 2023.09.30
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Abstract

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

Acknowledgement

We would like to thank the referees for valuable comments and suggestions which increases the understandability of the paper.

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