@article{Article_80,

title = {Transitive permutation groups with elements of movement three consecutive integers},

journal = {Communications in Combinatorics, Cryptography & Computer Science},

volume = {2024},

issue = {1},

issn = { 2783-5456 },

year = {2023},

url = {http://cccs.sgh.ac.ir/Articles/2024/issue 1/1-8-Transitivepermutationgroups.pdf},

author = {Bahman Askari},

keywords = {Permutation group, transitive, bounded movement, fixed point free element.},

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.}

};