Classification of a Class of Almost Completely Decomposable Groups

Multiplication Groups of Abelian Torsion-Free Groups of Finite Rank

“…A torsion-free group G of finite rank is called an almost completely decomposable group (an ACD-group) if G contains a completely decomposable subgroup of finite index. ACD-groups are studied in [1], [2], [3], [4], [6], [12], [15], [16], [18] The set of types We denote by A 0 the class of all reduced block-rigid CRQ-groups of ring type. In Section 2, we describe principal absolute ideals of groups in A 0 (Theorem 2.4).…”

Almost completely decomposable groups with primary regulator quotients and their endomorphism rings

“…In a special case, the decomposability properties determined by the rank of X/A were investigated in [4] for such groups. Note that the so-called "pathological" direct decompositions of acd groups X (which do not satisfy the near exchange property) occur only in the case where the regulator quotient X/R(X) is not primary (see [13,Theorems 90.1,90.2,90.3], [18, 13.1], [11], [20], [21], and also [2,3,5,9,10]). In contrast with this, some properties can be extended from groups X with primary X/R(X) to arbitrary acd groups.…”