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 finitely generated locally indicable group. For every $n \in \mathbb{N} $ there is a normal subgroup with index $n$. What can we say about residual finiteness of $G$?

share|cite|improve this question

Thompson's group $F$ has a normal subgroup of each finite index, just because it admits $\mathbf{Z}$ as a quotient, it is locally indicable (= every nontrivial f.g. subgroup admits $\mathbf{Z}$ as a quotient) but $F$ is not residually finite.

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.