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Keywords:
almost completely decomposable group; indecomposable; representation
almost completely decomposable group; indecomposable; representation
Summary:
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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