I read this theorem in the article which Antonio Beltran, I don't understand why prove this theorem:
"if a group $G$ satisfies $ν_{3}(G) = 1$ and has no composition factor isomorphic to the simple group $Sz(q)$, then G is solvable."
(which $ν_{p}(G)$ be the number of Sylow $p-$subgroups of $G$, and the only non-abelian simple finite groups whose order is not divisible by 3 are the Suzuki simple groups, Sz(q), with $q = 2^r$ and r > 1 odd).
I would be very thankful if you showed me ideas to prove.