an:01836147
Zbl 1015.20002
Ar??kan, A.
On barely transitive \(p\)-groups with soluble point stabilizer
EN
J. Group Theory 5, No. 4, 441-442 (2002).
00087209
2002
j
20B22
permutation groups; barely transitive groups; locally nilpotent groups; point stabilizers
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.
H.D.Macpherson (Leeds)