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An extension of commutativity degree of finite groups | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 آذر 1403 | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.26440.1616 | ||
| نویسنده | ||
| M. Hashemi* | ||
| Faculty of mathematical sciences, University of Guilan | ||
| چکیده | ||
| Let G be a finite group. The commutativity degree of G, written d(G), is defined as the ratio |{(x, y)|x, y \in G, xy = yx}|/|G|^2. In this paper, we first extend this concept of finite groups to the commutativity degree of fuzzy subgroups. Then, by using the numerical solutions of the equation xy − zu \eqiv t(mod n), we give explicit formulas for the commutativity degree of fuzzy subgroups of 2-generated groups of nilpotency class 2. Finally we show that this method also works for a large class of finite groups, including metabelian groups. | ||
| کلیدواژه‌ها | ||
| Finite groups؛ nilpotent groups؛ commutativity degree؛ fuzzy groups | ||
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آمار تعداد مشاهده مقاله: 146 |
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