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Doubly transitive groups in which a point stabilizer has an abelian normal subgroup

Let $G$ be a finite doubly transitive group in its action on the set $X$, such that a point stabilizer $G_x$ ($x \in X$) has an abelian normal subgroup $N_x$. I have read that if $\vert N_x \vert$ is ...
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Doubly transitive groups in which a one point stabilizer has a normal subgroup of even size

In 1972, Hering classified the finite doubly transitive permutation groups $(G,X)$ ($G$ acting faithfully on $X$) in which $G_x$, with $x \in X$, contains a normal subgroup $N_x$ of even order which ...
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