Abelian subgroup separability of certain generalized free products of free or finitely generated nilpotent groups

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• 作者：Wei Zhou^a ; ¹ ; ^{zh_great@swu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Goansu Kim^b ; ² ; ^{gskim@yu.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Primary ; 20E26 ; 20E06 ; secondary ; 20F10 ; 20F18
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：221
• 期：1
• 页码：222-228
• 全文大小：284 K

文摘

In this paper we prove that certain generalized free products of abelian subgroup separable groups, amalgamating an infinite cyclic subgroup, are abelian subgroup separable. Applying this, we derive that tree products of free groups or finitely generated nilpotent groups, amalgamating infinite cyclic subgroups, are abelian subgroup separable.