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On torsion-free barely transitive groups. (English) Zbl 0984.20001
A group $$G$$ is called barely transitive, if it acts transitively and faithfully on an infinite set and every orbit of every proper subgroup of $$G$$ is finite. The author shows that if $$G$$ is barely transitive and if the centralizer of a non-trivial element is infinite and contains the stabilizer of a point, then $$G$$ is not simple. Moreover, a barely transitive group $$G$$ is the union of an increasing sequence of proper normal subgroups if and only if $$G$$ is locally finite.
Reviewer: M.Droste (Dresden)

##### MSC:
 20B07 General theory for infinite permutation groups 20F50 Periodic groups; locally finite groups 20F24 FC-groups and their generalizations