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P-Nilpotent completion is not idempotent
Tan, Geok Choo

Data: 1997
Resum: Let P be an arbitrary set ofprimes. The P-nilpotent completion ofa group G is defined by the group homomorphism η : G → GP where GP = invlim(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 ofan 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 ofcircles is R-bad, where R is any subring ofrationals.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: Article ; recerca ; Versió publicada
Publicat a: Publicacions matemàtiques, V. 41 n. 2 (1997) p. 481-487, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/37908
DOI: 10.5565/PUBLMAT_41297_12

7 p, 110.5 KB

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