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The class of \((1,3)\)-groups with a homocyclic regulator quotient of exponent \(p^5\) is of finite representation type. (English) Zbl 1425.20027

Summary: The class of almost completely decomposable groups with a critical typeset of type \((1, 3)\) and a homocyclic regulator quotient of exponent \(p^5\) is shown to be of bounded representation type, i.e., in particular, a Remak-Krull-Schmidt class of torsion-free abelian groups. There are precisely 36 near-isomorphism classes of indecomposables all of rank \(\leq 9\).

MSC:

20K15 Torsion-free groups, finite rank
20K25 Direct sums, direct products, etc. for abelian groups
20K35 Extensions of abelian groups
15A21 Canonical forms, reductions, classification
16G60 Representation type (finite, tame, wild, etc.) of associative algebras
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References:

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