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Extension functors on the category of $$A$$-solvable abelian groups. (English) Zbl 0776.20018
Let $$A$$ and $$G$$ be abelian groups. The group $$H_ A(G)=\operatorname{Hom}(A,G)$$ has an $$E(A)$$-module structure in the natural way. Conversely, we set $$T_ A(M)= M\otimes_{E(A)}A$$ for any right $$E(A)$$-module $$M$$. The group $$G$$ is said to be $$A$$-solvable, if the natural evaluation map $$\theta_ G: T_ A H_ A(G)\to G$$ is an isomorphism. The author investigates some extension functors on the category $$C_ A$$ of $$A$$-solvable groups. The methods developed are used for a construction of $$A$$-solvable groups in the case that $$A$$ is slender and has rank at least two.
Reviewer: L.Bican (Praha)

##### MSC:
 20K40 Homological and categorical methods for abelian groups 16S50 Endomorphism rings; matrix rings 20K35 Extensions of abelian groups 20K30 Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups
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