Groups assembled from free and direct products

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Groups assembled from free and direct products

Let A be the collection of groups which can be assembled from infinite cyclic groups using the binary operations free and direct product. These groups can be described in several ways by graphs. The group (Z ∗Z)×(Z ∗Z) has been shown by [1] to have a rich subgroup structure. In this article we examine subgroups of A–groups. DefineA to be the smallest class of groups which contains the infinite ...

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An almost-direct product of free groups is an iterated semidirect product of finitely generated free groups in which the action of the constituent free groups on the homology of one another is trivial. We determine the structure of the cohomology ring of such a group. This is used to analyze the topological complexity of the associated Eilenberg-Mac Lane space. 1. Almost direct products of free...

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Subgroups of direct products of limit groups

If Γ1, . . . ,Γn are limit groups and S ⊂ Γ1 × · · · × Γn is of type FPn(Q) then S contains a subgroup of finite index that is itself a direct product of at most n limit groups. This answers a question of Sela.

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Complete Presentations of Direct Products of Groups

Complete presentations provide a natural solution to the word problem in monoids and groups. Here we give a simple way to construct complete presentations for the direct product of groups, when such presentations are available for the factors. Actually, the construction we are referring to is just the classical construction for direct products of groups, which has been known for a long time, bu...

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 1992

ISSN: 0012-365X

DOI: 10.1016/0012-365x(92)90279-o