Almost completely decomposable groups and unbounded representation type

Date

2012-01-01

Author

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

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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.

Subject Keywords

Representation, Indecomposable, Large rank, Almost completely decomposable group

URI

https://hdl.handle.net/11511/46863

Journal

JOURNAL OF ALGEBRA

DOI

https://doi.org/10.1016/j.jalgebra.2011.10.019

Collections

Department of Mathematics, Article

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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...
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(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.
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.

Citation Formats

D. M. Arnold, A. Mader, O. Mutzbauer, and E. Solak, “Almost completely decomposable groups and unbounded representation type,” JOURNAL OF ALGEBRA, pp. 50–62, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46863.