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

Let $G$ be a free group, if the action of $G$ on $\mathbb{R}$ is free, does it imply that $G$ is abelian?

share|cite|improve this question
I think this should come down mostly to definitions. – Newb Jun 13 '14 at 14:25
"the" action of $G$ on $\mathbb R$? Is there supposed to be a fixed action here? Are there any restrictions on this action in terms of the structure of $G$ and $\mathbb R$? – Dustan Levenstein Jun 13 '14 at 14:43

Hölder has proved that any group $G$ which acts freely on the real line by homeomorphisms is abelian.

share|cite|improve this answer

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.