There is a problem in Problems in Group Theory by J.D.Dixon :
2.51 If a permutation group $G$ contains a minimal normal subgroup $N$ which is both transitive and abelian, then $G$ is primitive.
He answered it amazingly:
Let $G_\alpha $ be a stabilizer of $G$. It is sufficient to show that $G_\alpha $ is a maximal subgroup of $G$. Let us suppose that, on the contrary, $G_\alpha $ is not a maximal subgroup of $G$. Then, there is a proper subgroup $K$ of $G$ properly containing $G_\alpha $. Since $K=K∩G_\alpha N=G_\alpha$ some $x≠1$ in $N$ lies in $K$. Therefore $K∩N = M$ is a nontrivial...
Is it possible we have an errata in $K=K∩G_\alpha N=G_\alpha$ cause of wrong typing or printing? Clearly, there would be an inconsistence with his assumption, and if so, which ones of the following would be the correct one:
$K⊇K∩G_\alpha N⊇G_\alpha$, or $K=K∩G_\alpha N⊇G_\alpha$
I will be so pleased if someone points the right one. I couldn’t find an erratum for this great book.