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Wreath product of permutation groups and their actions on a sets | ||
| Caspian Journal of Mathematical Sciences | ||
| مقاله 2، دوره 10، شماره 2، اسفند 2021، صفحه 142-155 اصل مقاله (94 K) | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2021.3053 | ||
| نویسنده | ||
| Nacer Ghadbane* | ||
| Laboratory of Pure and Applied Mathematics , Department of Mathematics, University of Msila, BP 166 Ichebilia, 28000, Msila, Algeria. | ||
| تاریخ دریافت: 06 آذر 1398، تاریخ بازنگری: 10 مهر 1399، تاریخ پذیرش: 15 مهر 1399 | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| group؛ acts of group in a set؛ morphism of groups؛ semi-direct product of groups؛ wreath product of groups | ||
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آمار تعداد مشاهده مقاله: 316 تعداد دریافت فایل اصل مقاله: 404 |
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