[Zurück]

Rostislav Grigorchuk, W. Herfort, P.A. Zalesskii et al.:
"The profinite completion of certain torsion p groups";
in: "Algebra. Proceedings of the International Conference to the 90th Birthday of A.G.Kurosh", I. Bahturin, A. Ol´shanski (Hrg.); Walter de Gruyter, Berlin-New York, 2000, (eingeladen), ISBN: 3-11-0163993, S. 113 - 123.

A rooted regular tree is a cycle free connected graph with constant degree of its vertices and a distinguished 'root'. Its automorphism group being an infinite wreath product, contains socalled fractal subgroups, most prominent the Grigorchuk's, Sidki's and Gupta's groups. For the class of such groups it is shown that they are all residually finite and their completion contains every countably generated pro-p group. The result is to be compared with the embedding of such groups in the Nottingham group.