For the class of K r separable (torsion-free abelian) groups, Kaplansky's Test Problems are investigated. Regarding the first problem, we obtain a positive answer for a large class of groups; and concerning the second problem, a negative answer for some class is found. A realization theorem for some rings äs endomorphism rings of K r separable groups is given and, äs usual, applied to the test problems to furnish negative answers to both problems for a class of groups.

This paper proposes a framework which supports the assessment and optimisation of the quality of products in very early phases of product development. First, an introduction is given to the notion of architecture and its establishment during the lifecycle process. Then a set of metrics is presented which is used to evaluate structural properties of a product architecture. This evaluation mechanism also serves to optimise a product structure towards an optimal representation of these properties. Finally we will show that structural properties support quality aspects that can be used to determine desirable product structures for a given design problem.

We show that the negation of the continuum hypothesis implies that the derived functor Bext 2 is not zero and there exist balanced subgroups of completely decomposable groups of rank ^i that are not Butler groups.

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