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We prove a pro-p version of the classical decomposition of a Zp-torsion free ZpCp-module into indecomposable modules. We also describe some pro-p ZpCpn modules obtained from a semidirect product of a free pro-p group F and a cyclic group Cpn of automorphisms by factoring out the (closed) commutator subgroup [F, F ].

Cyclic extensions of free pro-$p$ groups and $p$-adic modules