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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.

MSC:
20B22 Multiply transitive infinite groups
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[1] A. O. Asar.Barely transitive locally nilpotent p-groups. J. London Math. Soc. (2) 55 (1997), 357-362; Corrigendum, ibid. 61 (2000), 315-318. · Zbl 0897.20028
[2] A. O. Asar.Locally nilpotent p-groups whose proper subgroups are hypercentral or nilpotent-by-Chernikov. J. London Math. Soc. (2) 61 (2000), 412-422. · Zbl 0961.20031
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