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Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna
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p-Extensions of free pro-p groups
It is proved that a virtually free pro-p group G having a free pro-p subgroup of index p satisfies a pro-p version of the Dyer-Scott structure theorem (Comm. Alg. 3(3) (1975), 195–201). The pro-2 case had been settled by W. Herfort and P. Zalesskii in (manuscr. math. 93, 457–464 (1997)). A proof for (topologically) finitely generated G has been given by C. Scheiderer.
A consequence of our result is that for any automorphism of order pn of a free pro-p group its fixed point group is a free factor.
The main theorem generalizes Serre's well known result, stating that any virtually free torsion free pro-p group is free pro-p (Topology 3, 413–420, (1965)).
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