﻿ 立方自由次拟本原置换群

立方自由次拟本原置换群On Quasiprimitive Permutation Groups of Cube-Free Degree

Li和Seress [The primitive permutation groups of square-free degree, BULL. London Math. Soc. 35 (2003), 635-644]分类了平方自由次本原置换群。本文我们将给出立方自由次拟本原置换群的刻画，并提出几个关联的、有待进一步研究的问题。

Li and Seress [The primitive permutation groups of square-free degree, BULL. London Math. Soc. 35 (2003), 635-644] classified primitive permutation groups of square-free degree. In this paper, we will characterize quasiprimitive permutation groups of cube-free degree, and give several problems worth further research.

[1] Praeger, C.E. (1990) The Inclusion Problem for Finite Primitive Permutation Group. Proceedings of the London Mathematical Society, 60, 68-88.
http://dx.doi.org/10.1112/plms/s3-60.1.68

[2] Li, C.H. (2003) The Finite Primitive Permutation Groups Containing an Abelian Regular Subgroup. Proceedings of the London Mathematical Society, 87, 725-748.
http://dx.doi.org/10.1112/S0024611503014266

[3] Li, C.H. and Pan, J.M. Primitive Permutation Groups Containing a Transitive Metacyclic Subgroup. Submitted.

[4] Praeger, C.E. (1992) An O’Nan-Scott Theorem for Finite Quasiprimitive Permutation Groups and an Application to 2-Arc Transitive Graphs. Journal of the London Mathematical Society, 47, 227-239.

[5] Li, C.H. (2006) Finite Edge-Transitive Cayley Graphs and Rotary Cayley Maps. Transactions of the American Mathematical Society, 358, 4605-4635.
http://dx.doi.org/10.1090/S0002-9947-06-03900-6

[6] Li, C.H. and Seress, A. (2003) The Primitive Permutation Groups of Square-Free Degree. Bulletin of the London Mathematical Society, 35, 635-644.
http://dx.doi.org/10.1112/S0024609303002145

[7] Huppert, B. (1967) Finite Groups. Springer-Verlag, Berlin.

[8] Schur, I. (1907) Untersuchen über die Darstellung der endlichen Gruppen durch gebrochenen linearen Substitutionen. CreLLe J, 132, 85-137.

[9] Gorenstein, D. (1982) Finite Simple Groups. Plenum Press, New York.
http://dx.doi.org/10.1007/978-1-4684-8497-7

[10] Pan, J.M., Liu, Y., Huang, Z.H. and Liu, C.L. (2014) Tetrava-lent Edge-Transitive Graphs of Order p2q. Science in China Series B, 57, 293-302.
http://dx.doi.org/10.1007/s11425-013-4708-8

[11] Gorenstein, D. (1980) Finite Groups. 2nd Edition, AMS Publishing, American.

[12] Li, C.H. and Pan, J.M. (2007) Finite 2-Arc-Transitive Abelian Cayley Graphs. European Journal of Combinatorics, 29, 148-158.
http://dx.doi.org/10.1016/j.ejc.2006.12.001

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