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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)

20B07 General theory for infinite permutation groups
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20F24 FC-groups and their generalizations