IMCS/Publications/BASM/Issues/BASM n.2 (15), 1994/

On primitive solvable permutation groups with commutative stabilizer of a point. II. (Russian)

Authors: Shchukin K. K.


Let $\Theta$ be the stabilizer of point in the primitive subgroup $H$ of the symmetric group $S(E)$. If $\Theta$ contains a normal abelian subgroup $\Gamma$ acting as an irreducible subgroup on the normal abelian subgroup $T \not= 1$ of $H$, then $H$ is conjugated in $S(E)$ to the subgroup of the complete affinne grope of some field. In particular, $\Theta$ can be a splitting extension of $\Gamma$. The way of enumerating is proposed for the finite groups with this property.

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