I read this theorem in the article which Antonio Beltran, I don't understand why prove this theorem:
"we can easily prove (by induction on the order) that 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 by induction.