Geodesic
Indecomposable (1,3)-groups and a matrix problem
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 307-355.

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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 $k\geq 4$.
DOI : 10.1007/s10587-013-0020-6
Classification : 15A21, 16G20, 20K15, 20K25, 20K35
Keywords: almost completely decomposable group; indecomposable; representation 
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Arnold, David M.; Mader, Adolf; Mutzbauer, Otto; Solak, Ebru. Indecomposable (1,3)-groups and a matrix problem. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 307-355. doi : 10.1007/s10587-013-0020-6. http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0020-6/

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