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THE CLASS OF (2, 2)-GROUPS WITH HOMOCYCLIC REGULATOR QUOTIENT OF EXPONENT $p^{3}$ HAS BOUNDED REPRESENTATION TYPE

Part of: Representation theory of rings and algebras Abelian groups Basic linear algebra

Published online by Cambridge University Press:  04 December 2014

DAVID M. ARNOLD ,
ADOLF MADER ,
OTTO MUTZBAUER  and
EBRU SOLAK
DAVID M. ARNOLD
Affiliation:
Department of Mathematics, Baylor University, Waco, TX 76798-7328, USA email [email protected]
ADOLF MADER
Affiliation:
Department of Mathematics, University of Hawaii, 2565 McCarthy Mall, Honolulu, HI 96822, USA email [email protected]
OTTO MUTZBAUER
Affiliation:
Universität Würzburg, Mathematics Institute, Emil-Fischer-Str. 30, 97074 Würzburg, Germany email [email protected]
EBRU SOLAK*
Affiliation:
Department of Mathematics, Middle East Technical University, Üniversiteler Mah., Dumlupınar Bulvarı, No 1, 06800 Ankara, Turkey email [email protected]
*
✉[email protected]
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Abstract

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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.

Keywords

almost completely decomposable groupindecomposablebounded representation type

MSC classification

Primary: 20K15: Torsion-free groups, finite rank
Secondary: 20K25: Direct sums, direct products, etc. 20K35: Extensions 15A21: Canonical forms, reductions, classification 16G60: Representation type (finite, tame, wild, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 99 , Issue 1 , August 2015 , pp. 12 - 29
Copyright
© 2014 Australian Mathematical Publishing Association Inc. 

References

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