Geodesic
Sets with trivial global stabilizers for primitive permutation groups which are not almost simple
Trudy Instituta matematiki i mehaniki, Группы и графы, Tome 13 (2007) no. 1, pp. 115-131

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Let $G$ be a primitive permutation group on a finite set $X$ such that the global stabilizer of any subset of the set $X$ in the group $G$ is nontrivial. The description of $G$ is obtained in the case when $G$ is not almost simple. 
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     author = {A. V. Konygin},
     title = {Sets with trivial global stabilizers for primitive permutation groups which are not almost simple},
     journal = {Trudy Instituta matematiki i mehaniki},
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     publisher = {mathdoc},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2007_13_1_a8/}
}
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A. V. Konygin. Sets with trivial global stabilizers for primitive permutation groups which are not almost simple. Trudy Instituta matematiki i mehaniki, Группы и графы, Tome 13 (2007) no. 1, pp. 115-131. http://geodesic.mathdoc.fr/item/TIMM_2007_13_1_a8/