PROFINITE TOPOLOGIES IN FREE PRODUCTS OF GROUPS-Reference-Cited by-同舟云学术

PROFINITE TOPOLOGIES IN FREE PRODUCTS OF GROUPS

Published:2004-10 Issue:05n06 Volume:14 Page:751-772
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

RIBES LUIS¹,ZALESSKII PAVEL²

Affiliation:

1. School of Mathematics and Statistics, Carleton University, Ottawa, Ont., K1V 8N2, Canada

2. Departamento de Matematica, Universidade de Brasilia, Brasilia, Brazil

Abstract

Let [Formula: see text] be a nonempty class of finite groups closed under taking subgroups, quotients and extensions. We consider groups G endowed with their pro-[Formula: see text] topology, and say that G is 2-subgroup separable if whenever H and K are finitely generated closed subgroups of G, then the subset HK is closed. We prove that if the groups G1 and G2 are 2-subgroup separable, then so is their free product G1*G2. This extends a result to T. Coulbois. The proof uses actions of groups on abstract and profinite trees.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196704001992

Reference19 articles.

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