A subexponential bound on the cardinality of abelian quotients in finite transitive groups

We show that, for every transitive group $G$ of degree $n\ge 2$, the largest abelian quotient of $G$ has cardinality at most $4^{n\mathrm{/}\sqrt{{\log }_{2}n}}$. This gives a positive answer to a 1989 outstanding question of L'aszl'o Kov'acs and Cheryl Praeger.