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Barely transitive groups. (English) Zbl 1139.20034
A group \(G\) has a barely transitive representation if \(G\) acts on an infinite set \(\Omega\) transitively and faithfully and every orbit of every proper subgroup is finite. A group is called a barely transitive group if it has a barely transitive representation. This paper is a survey on barely transitive groups; it also involves some recent results in the case of a non-locally finite barely transitive group.

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