Indecomposable (1,3)-Groups and a matrix problem

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2013-06-01

Author

Arnold, David M.
Mader, Adolf
Mutzbauer, Otto
Solak, Ebru

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Almost completely decomposable groups with a critical typeset of type (1, 3) and a p-primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient p (k) , either no indecomposables if k a (c) 1/2 2; only six near isomorphism types of indecomposables if k = 3; and indecomposables of arbitrary large rank if k a (c) 3/4 4.

Subject Keywords

Almost completely, Decomposable group, Indecomposable, Representation

URI

https://hdl.handle.net/11511/32747

Journal

CZECHOSLOVAK MATHEMATICAL JOURNAL

DOI

https://doi.org/10.1007/s10587-013-0020-6

Collections

Department of Mathematics, Article

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Almost completely decomposable groups and unbounded representation type Arnold, David M.; Mader, Adolf; Mutzbauer, Otto; Solak, Ebru (2012-01-01) 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.
(1,4)-GROUPS WITH HOMOCYCLIC REGULATOR QUOTIENT OF EXPONENT p(3) Arnold, David M.; Mader, Adolf; Mutzbauer, Otto; Solak, Ebru (2015-01-01) The class of almost completely decomposable groups with a critical typeset of type (1,4) and a homocyclic regulator quotient of exponent p(3) is shown to be of bounded representation type. There are precisely four near-isomorphism classes of indecomposables, all of rank 6.
Classification of a class of torsion-free abelian groups Solak, Ebru (2016-01-01) 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.
REPRESENTATIONS OF POSETS AND INDECOMPOSABLE TORSION-FREE ABELIAN GROUPS Arnold, David; Mader, Adolf; Mutzbauer, Otto; Solak, Ebru (2014-03-04) 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.
Decomposition of a specific class of (1,3) groups Çölaşan, Utku Şükrü; Solak, Ebru; Department of Mathematics (2022-12-21) The classification (up to near isomorphism) of some class of almost completely decomposable groups with a regulating regulator is possible. Since almost completely decomposable groups can be written as a direct sum of indecomposable groups, for classification of almost completely decomposable groups it would be enough to find isomorphism classes of all indecomposable groups. The class of almost completely decomposable groups with a critical typeset in (1,3) configuration and a regulator quotient of exponent...

Citation Formats

D. M. Arnold, A. Mader, O. Mutzbauer, and E. Solak, “Indecomposable (1,3)-Groups and a matrix problem,” CZECHOSLOVAK MATHEMATICAL JOURNAL, pp. 307–355, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32747.