Seminar Talk

Characterizing virtually free pro-p groups that are topologically finitely generated

This is joint work with P.A. Zalesskii.
The following statements about a topologically finitely generated pro-p group G are equivalent: When G is free by cyclic of order p the result is due to Claus Scheiderer (1999). The ingredients of the proof of our result comprise the pro-p analog of Bass-Serre theory due to Mel'nikov-Zalesskii, Scheiderer's result, and, a deep result on p-adic representation theory by Alfred Weiss.

Profinite Groups

Basic material on profinite groups will be covered. I am indebted to my students Sema Alıcı and Berna Çınar for the Turkish translation.

Course Notes

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Tentative schedule

  1. Tue, 31.1.2012 Basic Definitions (Projective limit, examples like p-adic numbers, infinite Galois theory)
  2. Thu, 2.2.2012 Sylow theory of profinite groups (and, in the same vein, Hall theory of prosolvable groups)
  3. Fr, 3.2.2012 Profinite topology and profinite completion (and, slightly more general, pro-C completions)
  4. Mo, 6.2.2012 Free pro-C groups and the pro-C Kurosh subgroup theorem
  5. Tue, 7.2.2012 Free constructions, amalgamated free products and HNN-extensions
  6. We, 8.2.2012 Profinite graphs (finite graphs only) Fundamental pro-C groups of finite graphs of finite groups