Abstract
We prove that in the category of pro-p groups any finitely generated group G with a free open subgroup splits either as an amalgamated free product or as an HNN-extension over a finite p-group. From this result we deduce that such a pro-p group is the pro-p completion of a fundamental group of a finite graph of finite p-groups.
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To Oleg V. Mel’nikov and Luis Ribes
This research was partially supported by CNPq and CAPES.
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Herfort, W., Zalesskii, P. Virtually free pro-p groups. Publ.math.IHES 118, 193–211 (2013). https://doi.org/10.1007/s10240-013-0051-4
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DOI: https://doi.org/10.1007/s10240-013-0051-4