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

Coulbois, 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 -