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

We prove a pro-$p$ version of the classical decomposition of a $\mathbb{Z}_p$-torsion free $\mathbb{Z}_pC_p$-module into indecomposable modules. We also describe some pro-$p$ $\mathbb{Z}_pC_pn$-modules obtained from a semidirect product of a free pro-$p$ group $F$ and a cyclic group $ C_pn$ of automorphisms by factoring out the (closed) commutator subgroup [F, F].

Keywords

virtually free pro-$p$ groups. Pro-$p$ modules

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Published 9 January 2014