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 -
