Abstract
Infinite transitive permutation groups all proper subgroups of which have just finite orbits are treated. Under the extra condition of being locally finite, such groups are proved to be primary, and, moreover, soluble if the stabilizer of some point is soluble.
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REFERENCES
B. Hartley, “The normalizer condition and mini-transitive permutation groups,” Algebra Logika, 13, No. 5, 539–602 (1974).
V. V. Belyaev and M. Kuzucuoglu, “Barely transitive and Heineken–Mohamed groups,” J. London Math. Soc., II. Ser., 55,No. 2(176), 261–263 (1997).
V. V. Belyaev, “The existence problem for minimal non-FC-groups,” Sib. Math. Zh., 39, No. 6, 1267–1270 (1998).
F. A. Leinen, “Reduction theorem for perfect locally finite minimal non-FC-groups,” Glasg. Math. J., 41, No. 1, 81–83 (1999).
A. O. Azar, “Barely transitive locally nilpotent p-groups,” J. London Math. Soc., II. Ser., 55, No. 2(176), 357–362 (1997).
B. Hartley and M. Kuzucuoglu, “Non-simplicity of locally finite barely transitive groups,” Proc. Edinb. Math. Soc., II. Ser., 40, No. 3, 483–490 (1997).
M. Kuzucuoglu, “Barely transitive permutation groups,” Arch. Math., 55, No. 6, 521–532 (1990).
V. V. Belyaev, “Inert subgroups in infinite simple groups,” Sib. Mat. Zh., 34, No. 4, 17–23 (1993).
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Belyaev, V.V., Kuzucuoglu, M. Locally Finite Barely Transitive Groups. Algebra and Logic 42, 147–152 (2003). https://doi.org/10.1023/A:1023946008218
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DOI: https://doi.org/10.1023/A:1023946008218