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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.

20B22 Multiply transitive infinite groups
Full Text: DOI
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