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Displaying similar documents to “Equations in groups, with special emphasis on localization and torsion - II”

On induced morphism of Mislin genera.

Peter Hilton (1994)

Publicacions Matemàtiques

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Let N be a nilpotent group with torsion subgroup TN, and let α: TN → T' be a surjective homomorphism such that kerα is normal in N. Then α determines a nilpotent group Ñ such that TÑ = T' and a function α from the Mislin genus of N to that of Ñ in N (and hence Ñ) is finitely generated. The association α → α satisfies the usual functiorial conditions. Moreover [N,N] is finite if and only if [Ñ,Ñ] is finite and α is then a homomorphism of abelian groups. If Ñ belongs to the special class...

P-nilpotent completion is not idempotent.

Geok Choo Tan (1997)

Publicacions Matemàtiques

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Let P be an arbitrary set of primes. The P-nilpotent completion of a group G is defined by the group homomorphism η: G → G where G = inv lim(G/ΓG). Here ΓG is the commutator subgroup [G,G] and ΓG the subgroup [G, ΓG] 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 Z coefficients. Hence, P-nilpotent completion is not idempotent. Another important consequence of...

Groups with many nilpotent subgroups

Patrizia Longobardi, Mercede Maj, Avinoam Mann, Akbar Rhemtulla (1996)

Rendiconti del Seminario Matematico della Università di Padova

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