# P-nilpotent completion is not idempotent.

Publicacions Matemàtiques (1997)

- Volume: 41, Issue: 2, page 481-487
- ISSN: 0214-1493

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topTan, 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 > 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 > 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 -

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