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I'm reading the first chapter of Serre's Galois Cohomology.

On p. 58, He gives two examples of projective profinite groups:

  1. the profinite completion of free (discrete) groups;
  2. the cartesian product over all prime numbers of free pro-p groups.

Looking for other examples I understood solvable projective profinite groups.

Mimicking the construction of projective covers for modules, I found the concept of the projective cover of a profinite group.

Now I'm stuck!

Any suggestions of more examples of projective profinite groups?


EDIT: Actually I'd like to see finitely generated profinite groups. So, in other words, I want to know the finitely generated, closed subgroups of free profinite groups.

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Interesting question. I would give another +1, for "He"! –  Louis Burkill Apr 12 '12 at 22:41

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