It seems to be well-known that the six-transitive finite groups are the symmetric and alternating groups, and the only other four-transitive finite groups are the Mathieu groups (the statement can be found in Cameron's 1999 "Permutation Groups", p 110), but I can't seem to figure out where the result was first stated (Cameron is not much help, though he does give a vague sketch of how one might go about proving this result).



Where was it first stated that there are no 4-transitive finite groups other than symmetric, alternating and Mathieu groups?
In *Pacific Journal of Math* **4** (1954), pp 219-226, Marshall Hall, Jr. writes in the paper "On a theorem of Jordan" that:



> 
> In 1872, Jordan showed that a finite quadruply transitive group in which only the identity fixes four letters must be one of the following: the symmetric group on four or five letters, the alternating group on six letters, or the Mathieu group on eleven letters.
> 
> 
> 


(Hall's paper is [available from Project Euclid](http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.pjm/1103044881&page=record) ).


The citation is: C. Jordan, *Recherches sur les substitutions*, J. Math. Pures Appl. (2) **17** (1872), 351-363.


Hall generalizes the result to any group (finite or infinite) in which the stabilizer of four letters is finite of odd order. As I recall, he presents the result extending it from 4-transitive to $k$-transitive (with $k\gt 3$) in his book *The Theory of Groups*, but I'm away from the office this week and unable to verify this.


