Weak potency and cyclic subgroup separability of certain free products and tree products
Document Type
Article
Publication Date
9-1-2023
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
Generalized free products, tree products, weakly potent, cyclic subgroup separable, residually finite
Divisions
MathematicalSciences
Publication Title
Bulletin of the Korean Mathematical Society
Volume
60
Issue
5
Publisher
Korean Mathematical Society
Publisher Location
KOREA SCIENCE TECHNOLOGY CTR 202, 635-4 YEOKSAM-DONG, KANGNAM-KU, SEOUL 135-703, SOUTH KOREA