# A note on the continuous extensions of injective morphisms between free groups to relatively fre profinite groups.

Thierry Coulbois; Mark Sapir; Pascal Weil

Publicacions Matemàtiques (2003)

- Volume: 47, Issue: 2, page 477-487
- ISSN: 0214-1493

## Access Full Article

top## Abstract

top## How to cite

topCoulbois, Thierry, Sapir, Mark, and Weil, Pascal. "A note on the continuous extensions of injective morphisms between free groups to relatively fre profinite groups.." Publicacions Matemàtiques 47.2 (2003): 477-487. <http://eudml.org/doc/41465>.

@article{Coulbois2003,

abstract = {Let V be a pseudovariety of finite groups such that free groups are residually V, and let φ: F(A) → F(B) be an injective morphism between finitely generated free groups. We characterize the situations where the continuous extension φ' of φ between the pro-V completions of F(A) and F(B) is also injective. In particular, if V is extension-closed, this is the case if and only if φ(F(A)) and its pro-V closure in F(B) have the same rank. We examine a number of situations where the injectivity of φ' can be asserted, or at least decided, and we draw a few corollaries.},

author = {Coulbois, Thierry, Sapir, Mark, Weil, Pascal},

journal = {Publicacions Matemàtiques},

keywords = {Teoría de grupos; Grupos libres; Grupos finitos; profinite groups; pseudovarieties of finite groups; free groups},

language = {eng},

number = {2},

pages = {477-487},

title = {A note on the continuous extensions of injective morphisms between free groups to relatively fre profinite groups.},

url = {http://eudml.org/doc/41465},

volume = {47},

year = {2003},

}

TY - JOUR

AU - Coulbois, Thierry

AU - Sapir, Mark

AU - Weil, Pascal

TI - A note on the continuous extensions of injective morphisms between free groups to relatively fre profinite groups.

JO - Publicacions Matemàtiques

PY - 2003

VL - 47

IS - 2

SP - 477

EP - 487

AB - Let V be a pseudovariety of finite groups such that free groups are residually V, and let φ: F(A) → F(B) be an injective morphism between finitely generated free groups. We characterize the situations where the continuous extension φ' of φ between the pro-V completions of F(A) and F(B) is also injective. In particular, if V is extension-closed, this is the case if and only if φ(F(A)) and its pro-V closure in F(B) have the same rank. We examine a number of situations where the injectivity of φ' can be asserted, or at least decided, and we draw a few corollaries.

LA - eng

KW - Teoría de grupos; Grupos libres; Grupos finitos; profinite groups; pseudovarieties of finite groups; free groups

UR - http://eudml.org/doc/41465

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.