Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

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

Is there an action (which turns out to be useful) of a group $G$ on the set (or isomorphism classes) of its finite quotients?

share|cite|improve this question
Does it have to be the group $G$ itself? $\text{Out}(G)$ acts on the set of finite-index normal subgroups in an obvious way. – Qiaochu Yuan Aug 5 '11 at 1:45

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.