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On barely transitive $$p$$-groups with soluble point stabilizer. (English) Zbl 1015.20002
A permutation group on an infinite set is ‘barely transitive’ if it is infinite but each orbit of each proper subgroup is finite. The author shows that if $$G$$ is a barely transitive locally nilpotent $$p$$-group and a point stabilizer in $$G$$ is soluble, then $$G'<G$$. This extends an earlier result of A. O. Asar, who assumed in addition that the point stabilizer is hypercentral.

##### MSC:
 20B22 Multiply transitive infinite groups
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##### References:
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