P-nilpotent completion is not idempotent.

Título inglés P-nilpotent completion is not idempotent.
Título español El completo nilpotente P no es idempotente.
Autor/es Tan, Geok Choo
Organización Dep. Math. Fac. Sci. Nat. Univ. Singapore, Singapur, Singapur
Revista 0214-1493
Publicación 1997, 41 (2): 481-487, 9 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés Let P be an arbitrary set of primes. The P-nilpotent completion of a group G is defined by the group homomorphism η: G → GP' where GP' = inv lim(G/ΓiG)P. Here Γ2G is the commutator subgroup [G,G] and ΓiG the subgroup [G, Γi−1G] when i > 2. In this paper, we prove that P-nilpotent completion of an infinitely generated free group F does not induce an isomorphism on the first homology group with ZP coefficients. Hence, P-nilpotent completion is not idempotent. Another important consequence of the result in homotopy theory (as in [4]) is that any infinite wedge of circles is R-bad, where R is any subring of rationals.
Clasificación UNESCO 120106
Palabras clave español Grupo nilpotente ; Teoría de la localización
Código MathReviews MR1485497
Icono pdf Acceso al artículo completo