For a project for one of our subjects we have to write about a certain topic. Our topic is very transitive groups. This means a permutation group on the natural integers, that is $k$-transitive for every $k$.

One of the questions we have to try to answer about this subject is, if there is a list with all the examples for this special kind of group. Since we are having a hard time finding an answer on the internet we hope that you guys can help us.