Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.