The Classification of Permutation Groups with Maximum Orbits

  • Behname Razzaghmaneshi Islamic Azad University
Keywords: permutation group, bounded movement, orbits, permutation group, bounded movement, orbits

Abstract

Let G be a permutation group on a set with no fixed points in and let m be a positive integer. If no element of G moves any subset of by more than m points (that is, if Capture15.JPGfor every and g 2 G), and the lengths two of orbits is p, and the restof orbits have lengths equal to 3. Then the number t of G-orbits in is at most Capture21.JPG Moreover, we classifiy all groups forCapture31.JPG is hold.(For Capture4.JPG denotes the greatest integer less than or equal to x.)

Author Biography

Behname Razzaghmaneshi, Islamic Azad University

Department of Mathematics
Islamic Azad University,Talesh Branch,Talesh, Iran

References

L. Brailovsky, Structure of quasi-invariant sets, Arch. Math.,59 (1992),322- 326.

L. Brailovsky, D. Pasechnix , C. E. Praeger, Subsets close to invarianr subset of quasi-invariant subsets for group actions ,,Proc. Amer. Math.Soc. ,123(1995),2283-2295.

C. E. Praeger,On permutation groups with bounded movement,J.Algebra ,144(1991),436-442.

C. E. Praeger, The separation theorem for group actions, in ”ordered Groups and Infinite Groups”(W. charles Holland, Ed.), Kluwer Academic, Dordrecht/ Boston/ Lond, 1995.

A. Hassani, M. Khayaty, E. I. Khukhro and C. E. Praeger, Transitive permutation groups with bounded movement having maximum degree. J. Algebra,214(1999),317-337.

J. R. Cho, P.S.Kim, and C. E. Praeger, The maximal number of orbits of a permutation Group with Bounded Movement, J.Algebra,214 (1999),625- 630.

P. M. Neumann, The structure of finitary Permutation groups, Arch. Math. (Basel) 27(1976),3-17.

B. H. Neumann, Groups covered by permutable subsets, J. London Math soc., 29(1954), 236-248.

P. M. Neumann, C. E. Praeger, On the Movement of permutation Group, J. Algebra, 214, (1999)631-635.

Published
2018-12-31
How to Cite
Razzaghmaneshi, B. (2018). The Classification of Permutation Groups with Maximum Orbits. JOURNAL OF ADVANCES IN MATHEMATICS, 15, 8155-8161. https://doi.org/10.24297/jam.v15i0.7926
Section
Articles