Abstract
The absolute radical of an Abelian group G is the intersection of radicals of all associative rings with additive group G. L. Fuchs formulated the problem on a description of absolute radicals of Abelian groups. For a group from some class of almost completely decomposable Abelian groups the absolute Jacobson radical is described. In the class of almost completely decomposable Abelian groups semisimple groups are described.
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