Indecomposable Decompositions of Torsion-free Abelian Groups

2018/02/27 by Mader, Adolf, Schultz, Phill
#20K15 #20K25 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1802.09768

Abstract

An indecomposable decomposition of a torsion-free abelian group G of rank n is a decomposition G=A₁⊕⋯⊕ A_t where A_i is indecomposable of rank r_i so that ∑_i r_i=n is a partition of n. The group G may have decompositions that result in different partitions of n. We address the problem of characterising those sets of partitions of n which can arise from indecomposable decompositions of a torsion-free abelian group.

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