The object of wreath product of permutation groups is defined the actions on cartesian product of two sets. In this paper we consider S(Γ) and S(Δ) be permutation groups on Γ and Δ respectively, and S(Γ)^{Δ} be the set of all maps of Δ into the permutations group S(Γ). That is S(Γ)^{Δ}={f:Δ→S(Γ)}. S(Γ)^{Δ} is a group with respect to the multiplication defined by for all δ in Δ by (f₁f₂)(δ)=f₁(δ)f₂(δ). After that, we introduce the notion of S(Δ) actions on S(Γ)^{Δ} : S(Δ)×S(Γ)^{Δ}→S(Γ)^{Δ},(s,f)↦s⋅f=f^{s}, where f^{s}(δ)=(f∘s⁻¹)(δ)=(fs⁻¹)(δ) for all δ∈Δ. Finaly, we give the wreath product W of S(Γ) by S(Δ), and the action of W on Γ×Δ.
Ghadbane, N. (2021). Wreath product of permutation groups and their actions on a sets. Caspian Journal of Mathematical Sciences, 10(2), 142-155. doi: 10.22080/cjms.2021.3053
MLA
Nacer Ghadbane. "Wreath product of permutation groups and their actions on a sets", Caspian Journal of Mathematical Sciences, 10, 2, 2021, 142-155. doi: 10.22080/cjms.2021.3053
HARVARD
Ghadbane, N. (2021). 'Wreath product of permutation groups and their actions on a sets', Caspian Journal of Mathematical Sciences, 10(2), pp. 142-155. doi: 10.22080/cjms.2021.3053
VANCOUVER
Ghadbane, N. Wreath product of permutation groups and their actions on a sets. Caspian Journal of Mathematical Sciences, 2021; 10(2): 142-155. doi: 10.22080/cjms.2021.3053
)