Título inglés |
A note on the continuous extensions of injective morphisms between free groups to relatively fre profinite groups. |
Título español |
Una nota sobre las extensiones continuas de morfismos inyectivos entre grupos libres y grupos profinitos relativamente libres. |
Autor/es |
Coulbois, Thierry ; Sapir, Mark ; Weil, Pascal |
Organización |
Equipe Log. Univ. Paris-7, Paris, Francia;Univ. Al-Quds, Occup. Palestinian Territ., Palestina;Dep. Math. Vanderbilt Univ., Nashville Tennessee, Estados Unidos;LaBRI [CNRS], Talence, Francia |
Revista |
0214-1493 |
Publicación |
2003, 47 (2): 477-487, 12 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
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. |
Clasificación UNESCO |
120106 |
Palabras clave español |
Teoría de grupos ; Grupos libres ; Grupos finitos |
Código Z-Math |
Zbl 1064.20028 |
Acceso al artículo completo |