Original Research Article

Article volume = 2024 and issue = 1

Pages: 52–59

Article publication Date: December 09, 2023

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# Transitive permutation groups with elements of movement three consecutive integers

#### Bahman Askari

Department of Mathematics, Qorveh Branch, Islamic Azad University, Qorveh, Iran.

##### Abstract:

Let G be a permutation group on a set Ω with no fixed point in Ω and let m be a positive integer. If for each subset Γ of Ω the size |Γg \ Γ | is bounded, for g ∈ G, we define the movement of g as the max |Γg \ Γ | over all subsets Γ of Ω, and the movement of G is defined as the maximum of move(g) over all non-identity elements of g ∈ G. In this paper we classify all transitive permutation groups with bounded movement equal to m that are not a 2−group, but in which every non-identity element has the movement m, m−1 or m−2.

##### Keywords:

Permutation group, transitive, bounded movement, fixed point free element.

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##### Cite this article as:

- Bahman Askari, Transitive permutation groups with elements of movement three consecutive integers, Communications in Combinatorics, Cryptography & Computer Science, 2024(1), PP.52–59, 2023
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