Abstract
Let G be a permutation group on a set withno fixed points in and let m be a positive integer. If for each subset T of the size |Tg\T| is bounded, for gEG, we define the movement of g as the max|Tg\T| over all subsets T of . In this paper we classified all of permutation groups on set of size 3m + 1 with 2 orbits such that has movement m . 2000 AMS classification subjects: 20B25
Highlights
Let G be a transitive permutation group on a set Ω such that G is not 2-group and let m be a positive integer
In [ ], C.E.Oraeger shown that if |Γg \ Γ| ≤ m for every subset Γ of Ω and all g ∈ G, | Ω |≤
If for a subset Γ of Ω the size |Γg \ Γ| is bounded, for g ∈ G, we define the movement of Γ as move(Γ) = maxg∈G|Γg \ Γ|
Summary
Let G be a transitive permutation group on a set Ω such that G is not 2-group and let m be a positive integer. We show that if G be a intrasitve permutation group on set Ω of size 3m + 1 with 2 orbits such that has movement m, and let B is the semi-direct product of Z22.Z3. G is satisfy one of the following : G1 = B ×Hd or G2 = A4 × Hd, where H = Z3 or S3, d = m − 2, and A4 is the permutation group on 4 elements.
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