Residual Separability of Subgroups in Free Products with Amalgamated Subgroup of Finite Index

Сибирский математический журнал

A. A. Kryazheva¹ 

[1] Ivanovo State University

关键词: residually separable subgroup;    residually finite group;    free product;    split extension;   

DOI  :  10.1134/S0037446619020125

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

Let P be the free product of groups A and B with amalgamated subgroup H, where H is a proper subgroup of finite index in A and B. We assume that the groups A and B satisfy a nontrivial identity and for each natural n the number of all subgroups of index n in A and B is finite. We prove that all cyclic subgroups in P are residually separable if and only if P is residually finite and all cyclic subgroups in H are residually separable; and all finitely generated subgroups in P are residually separable if and only if P is residually finite and all subgroups that are the intersections of H with finitely generated subgroups of P are finitely separable in H.

【 授权许可】

CC BY