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

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
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