WEAK POTENCY AND CYCLIC SUBGROUP SEPARABILITY OF CERTAIN FREE PRODUCTS AND TREE PRODUCTS

被引：0
|
作者：
Asri, Muhammad Sufi Mohd [1 ]
Othman, Wan Ainun Mior [1 ]
Wong, Kok Bin [1 ]
Wong, Peng Choon [1 ]
机构：
[1] Univ Malaya, Inst Math Sci, Fac Sci, Kuala Lumpur 50603, Malaysia
来源：
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2023年 / 60卷 / 05期
关键词：
Generalized free products; tree products; weakly potent; cyclic subgroup separable; residually finite; GENERALIZED FREE-PRODUCTS; POLYGONAL PRODUCTS; CONJUGACY SEPARABILITY; RESIDUAL FINITENESS; GRAPHS;
D O I：
10.4134/BKMS.b220715
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：1375 / 1390
页数：16
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