(1,4)-GROUPS WITH HOMOCYCLIC REGULATOR QUOTIENT OF EXPONENT p(3)

Date

2015-01-01

Author

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

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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.

Subject Keywords

Almost completely decomposable group, Indecomposable, Bounded representation type

URI

https://hdl.handle.net/11511/32899

Journal

COLLOQUIUM MATHEMATICUM

DOI

https://doi.org/10.4064/cm138-1-8

Collections

Department of Mathematics, Article

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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.
Indecomposable (1,3)-Groups and a matrix problem Arnold, David M.; Mader, Adolf; Mutzbauer, Otto; Solak, Ebru (2013-06-01) 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.
THE CLASS OF (2,2)-GROUPS WITH HOMOCYCLIC REGULATOR QUOTIENT OF EXPONENT p(3) HAS BOUNDED REPRESENTATION TYPE Arnold, David M.; Mader, Adolf; Mutzbauer, Otto; Solak, Ebru (Cambridge University Press (CUP), 2015-08-01) The class of almost completely decomposable groups with a critical typeset of type (2,2) and a homocyclic regulator quotient of exponent p(3) is shown to be of bounded representation type. There are only 16 isomorphism at p types of indecomposables, all of rank 8 or lower.
The class of (1,3)-groups with homocyclic regulator quotient of exponent p(4) has bounded representation type Arnold, David M.; Mader, Adolf; Mutzbauer, Otto; Solak, Ebru (Elsevier BV, 2014-02-15) The class of almost completely decomposable groups with a critical typeset of type (1,3) and a homocyclic regulator quotient of exponent p(4) is shown to be of bounded representation type. There are only nine near-isomorphism types of indecomposables, all of rank <= 6.
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.

Citation Formats

D. M. Arnold, A. Mader, O. Mutzbauer, and E. Solak, “(1,4)-GROUPS WITH HOMOCYCLIC REGULATOR QUOTIENT OF EXPONENT p(3),” COLLOQUIUM MATHEMATICUM, pp. 131–144, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32899.