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Classification of a class of torsion-free abelian groups
Date
2016-01-01
Author
Solak, Ebru
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The class of almost completely decomposable groups with a critical typeset of type (2, 2) and a regulator quotient of exponent <= p(2) is shown to have exactly 4 near-isomorphism classes of indecomposable groups. Every group of the class is up to near-isomorphism uniquely a direct sum of these four indecomposable groups.
Subject Keywords
Almost Completely Decomposable Group;
,
İndecomposable
,
Bounded Representation Type
URI
https://hdl.handle.net/11511/48673
Journal
RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA
DOI
https://doi.org/10.4171/rsmup/135-6
Collections
Department of Mathematics, Article
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Representations of posets in certain modules are used to find indecomposable almost completely decomposable torsion-free abelian groups. For a special class of almost completely decomposable groups we determine the possible ranks of indecomposable groups and show that the possible ranks are realized by indecomposable groups in the class.
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Almost completely decomposable groups with a regulating regulator and a p-primary regulator quotient are studied. It is shown that there are indecomposable such groups of arbitrarily large rank provided that the critical typeset contains some basic configuration and the exponent of the regulator quotient is sufficiently large.
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E. Solak, “Classification of a class of torsion-free abelian groups,”
RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA
, pp. 111–131, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48673.