چكيده به لاتين
Let G be a permutation group on a set Ω with no fixed points in Ω and let m be a positive integer. Let Γ ⊆ Ω. If for each g ∈ G the size |Γg⧹Γ| is bounded, we define the movement of Γ as move(Γ) = maxg∈G|Γg − Γ|. If move(Γ) ≤ m for all Γ ⊆ Ω, then G is said to have bounded movement and the movement of G is defined as the maximum of move(Γ) over all non-empty subset Γ ⊂ Ω. Similarly, for each 1 ≠ g ∈ G, we define the movement of g as max|Γg⧹Γ| over all subsets Γ of Ω. By using GAP system, we can describe each element of a transitive group as a product of disjoint cycles. In this thesis we will classify all transitive permutation groups with movement m and maximum bound, or each element has movement with some conditions. In particular, we will investigate all transitive permutation groups G with bounded movement equal to m such that G is not a 2-group but in which every non-identity element has the movement m or m − 1, every non- identity element has the movement m or m − 2, and every non-identity element of movement three consecutive integers.
