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| Movement of Intransitive Permutation Groups Having Maximum Degree |
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Citation： |
Mehdi ALAEIYAN,Mehdi REZAEI.Movement of Intransitive Permutation Groups Having Maximum Degree[J].Chinese Annals of Mathematics B,2012,33(1):143~148 |
| Page view： 2789
Net amount： 1897 |
Authors： |
Mehdi ALAEIYAN; Mehdi REZAEI; |
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| Abstract： |
Let G be a permutation group on a set Ω with no fixed points in Ω, and m be apositive integer. Then the movement of G is defined as move(G):=supΓ{|Γg \Γ| | g ∈ G}. Itwas shown by Praeger that if move(G) = m, then |Ω| _ 3m+ t?1, where t is the numberof G-orbits on Ω. In this paper, all intransitive permutation groups with degree 3m+t?1which have maximum bound are classified. Indeed, a positive answer to her question thatwhether the upper bound |Ω| = 3m + t ? 1 for |Ω| is sharp for every t > 1 is given. |
Keywords： |
Intransitive permutation groups, Bounded movement, Orbit |
Classification： |
20B05 |
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