Abstract
Let F be a free pro-p group of finite rank n and \({C_{p^r}}\) a cyclic group of order p r. In this work we classify p-adic representations \({ C_{p^r}\longrightarrow GL_n(\mathbb{Z}_{p})}\) that can be obtained as a composite of an embedding \({C_{p^r}\longrightarrow {\rm Aut}(F)}\) with the natural epimorphism \({{\rm Aut}(F)\longrightarrow GL_n(\mathbb{Z}_{p})}\) .
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A. L. P. Porto and P. A. Zalesskii were supported by CNPq.
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Porto, A.L.P., Zalesskii, P.A. Free-by-finite pro-p groups and integral p-adic representations. Arch. Math. 97, 225–235 (2011). https://doi.org/10.1007/s00013-011-0294-6
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DOI: https://doi.org/10.1007/s00013-011-0294-6