P-nilpotent completion is not idempotent.

Tan, Geok Choo. "P-nilpotent completion is not idempotent.." Publicacions Matemàtiques 41.2 (1997): 481-487. <http://eudml.org/doc/41311>.

@article{Tan1997,
abstract = {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 &gt; 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.},
author = {Tan, Geok Choo},
journal = {Publicacions Matemàtiques},
keywords = {Grupo nilpotente; Teoría de la localización; -nilpotent completions; infinitely generated free groups; first homology groups; wedges of circles},
language = {eng},
number = {2},
pages = {481-487},
title = {P-nilpotent completion is not idempotent.},
url = {http://eudml.org/doc/41311},
volume = {41},
year = {1997},
}

TY - JOUR
AU - Tan, Geok Choo
TI - P-nilpotent completion is not idempotent.
JO - Publicacions Matemàtiques
PY - 1997
VL - 41
IS - 2
SP - 481
EP - 487
AB - 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 &gt; 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.
LA - eng
KW - Grupo nilpotente; Teoría de la localización; -nilpotent completions; infinitely generated free groups; first homology groups; wedges of circles
UR - http://eudml.org/doc/41311
ER -