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Displaying similar documents to “On induced morphism of Mislin genera.”

On a theorem of Schur.

Hilton, Peter (2001)

International Journal of Mathematics and Mathematical Sciences

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On finite abelian groups realizable as Mislin genera.

Peter Hilton, Dirk Scevenels (1997)

Publicacions Matemàtiques

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We study the realizability of finite abelian groups as Mislin genera of finitely generated nilpotent groups with finite commutator subgroup. In particular, we give criteria to decide whether a finite abelian group is realizable as the Mislin genus of a direct product of nilpotent groups of a certain specified type. In the case of a positive answer, we also give an effective way of realizing that abelian group as a genus. Further, we obtain some non-realizability results.

Some remarks on almost finitely generated nilpotent groups.

Peter Hilton, Robert Militello (1992)

Publicacions Matemàtiques

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We identify two generalizations of the notion of a finitely generated nilpotent. Thus a nilpotent group G is fgp if Gp is fg as p-local group for each p; and G is fg-like if there exists a fg nilpotent group H such that Gp ≅ Hp for all p. The we have proper set-inclusions: {fg} ⊂ {fg-like} ⊂ {fgp}. We examine the extent to which fg-like nilpotent groups satisfy the axioms for...

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...