Intransitive Permutation Groups with Bounded Movement Having Maximum Degree


  • Behnam Razzagh  Islamic Azad University



Let G be a permutation group on a set withUntitled4.pngno fixed points in Untitled5.pngand let m be a positive integer. If for each subset T of Untitled6.pngthe  size |Tg\T| is bounded, for gEG, we define the movement of g as the max|Tg\T| over all subsets T of Untitled6.png . In this paper we classified all of permutation groups on set Untitled6.png   of size 3m + 1 with 2 orbits such that has movement m . 2000 AMS classification subjects: 20B25


Download data is not yet available.

Author Biography

Behnam Razzagh,  Islamic Azad University

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


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.

A.Gardiner,C.E.Praeger,Transitive permutation groups with bounded movement,J.Algebra 168(1994)798-803.

A.Mann,C.E.Praeger,ransitive permutation groups of minimal movement, J.Algebra 181(1996)903-911.

H.Wielandt,Finite Permutation Groups,Academic Press,NewYork,1968.

P.S.Kim, Y.Kim,Certain groups with bounded movement having the maximal number of orbits,J.Algebra 252(2002)74-83.

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.

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. 7

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




How to Cite

Razzagh, B. (2019). Intransitive Permutation Groups with Bounded Movement Having Maximum Degree. JOURNAL OF ADVANCES IN MATHEMATICS, 16, 8340–8347.