Description of Barely Transitive Groups with Soluble Point Stabilizer
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We describe the barely transitive groups with abelian-by-finite, nilpotent-by-finite and soluble-by-finite point stabilizer. In article  Hartley asked whether there is a torsionfree barely transitive group. One consequence of our results is that there is no torsionfree barely transitive group whose point stabilizer is nilpotent. Moreover, we show that if the stabilizer of a point is a permutable subgroup of an infinitely generated barely transitive group G, then G is locally finite.