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.
@article{PMIHES_2013__118__193_0, author = {Herfort, Wolfgang and Zalesskii, Pavel}, title = {Virtually free pro-\protect\emph{p} groups}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {193--211}, publisher = {Springer Berlin Heidelberg}, address = {Berlin/Heidelberg}, volume = {118}, year = {2013}, doi = {10.1007/s10240-013-0051-4}, mrnumber = {3150249}, zbl = {1288.20037}, language = {en}, url = {http://www.numdam.org/articles/10.1007/s10240-013-0051-4/} }
TY - JOUR AU - Herfort, Wolfgang AU - Zalesskii, Pavel TI - Virtually free pro-p groups JO - Publications Mathématiques de l'IHÉS PY - 2013 SP - 193 EP - 211 VL - 118 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - http://www.numdam.org/articles/10.1007/s10240-013-0051-4/ DO - 10.1007/s10240-013-0051-4 LA - en ID - PMIHES_2013__118__193_0 ER -
%0 Journal Article %A Herfort, Wolfgang %A Zalesskii, Pavel %T Virtually free pro-p groups %J Publications Mathématiques de l'IHÉS %D 2013 %P 193-211 %V 118 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U http://www.numdam.org/articles/10.1007/s10240-013-0051-4/ %R 10.1007/s10240-013-0051-4 %G en %F PMIHES_2013__118__193_0
Herfort, Wolfgang; Zalesskii, Pavel. Virtually free pro-p groups. Publications Mathématiques de l'IHÉS, Tome 118 (2013), pp. 193-211. doi : 10.1007/s10240-013-0051-4. http://www.numdam.org/articles/10.1007/s10240-013-0051-4/
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