# 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

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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 -