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 |
Acceso al artículo completo |