ScholarLens Back to search
2004•International Journal of Algebra and ComputationRequires access

PROFINITE TOPOLOGIES IN FREE PRODUCTS OF GROUPS

Luis Ribes, Pavel Zalesskii

Open publisher page 6 citations

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.

About this research paper

What this paper is about

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.

Why it matters

OpenAlex reports 6 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available 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.

Key concepts: Mathematics, Profinite group, Free product, Separable space, Quotient, Finitely-generated abelian group, Combinatorics, Topological group

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
PROFINITE TOPOLOGIES IN FREE PRODUCTS OF GROUPS — Research Paper | ScholarLens