Let $G$ be a finite nonabelian simple group.
We call $G$ a $K\_3$-group if $|G|=p^aq^br^c$ where $p,q,r$ are distinct primes and $a,b,c$ are positive integers.


**My question is: Is there a CFSG-free proof of the classification of simple $K\_3$-groups?**


Any explanation, references, suggestion and examples are appreciated.



CFSG-free proof for classifying simple $K_3$-group
By the Feit-Thompson theorem, one of the primes has to be two. Then by John Thompson's N-group classification (1970-1973), the three primes have to come from a very short list of triples. The various cases were then worked out by Geoff Mason, David Wales, and Jeff Leon in the seventies. This should give you enough information to get the references from MR.


