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

Andrea Lucchini, Luca Sabatini, Pablo Spiga

We show that, for every transitive group $G$ of degree $n\ge 2$, the largest abelian quotient of $G$ has cardinality at most $4^{n/\sqrt{{\log }_{2}n}}$. This gives a positive answer t…