Products of finite nilpotent groups.

Hermann Heineken

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Some remarks on almost finitely generated nilpotent groups.

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We identify two generalizations of the notion of a finitely generated nilpotent. Thus a nilpotent group G is fgp if G_p is fg as p-local group for each p; and G is fg-like if there exists a fg nilpotent group H such that G_p ≅ H_p 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...

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Groups with the Minimal Condition on Non-“Nilpotent-by-Finite” Subgroups

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We characterize the groups which do not have non-trivial perfect sections and such that any strictly descending chain of non-“nilpotent-by-finite” subgroups is finite.