Free-by-finite pro-p groups and integral p-adic representations

Abstract

Let F be a free pro-p group of finite rank n and Cpr a cyclic group of order p r . In this work we classify p-adic representations Cpr −→ GLn(Zp) that can be obtained as a composite of an embedding Cpr −→ Aut(F ) with the natural epimorphism Aut(F ) −→ GLn(Zp).Mathematics Subject Classification (2010). Primary 20E18, 20C11.

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

“…Note that for n > 1, F ab does not give all possible Z p -torsion free pro-p Z p C pmodules, see Remark 4.5 in [8].…”