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(1,4)-groups with homocyclic regulator quotient of exponent p³

David M. Arnold; Adolf Mader; Otto Mutzbauer; Ebru Solak — 2015

Colloquium Mathematicae

The class of almost completely decomposable groups with a critical typeset of type (1,4) and a homocyclic regulator quotient of exponent p³ is shown to be of bounded representation type. There are precisely four near-isomorphism classes of indecomposables, all of rank 6.

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

David M. Arnold; Adolf Mader; Otto Mutzbauer; Ebru Solak — 2013

Czechoslovak Mathematical Journal

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 $k \leq 2$ ; only six near isomorphism types of indecomposables if $k = 3$ ; and indecomposables of arbitrary large rank if $k \geq 4$ .

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