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The probability that two elements of a group have the same centralizers | ||
| International Journal of Group Theory | ||
| دوره 14، شماره 4، اسفند 2025، صفحه 223-233 اصل مقاله (420.71 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2024.142171.1912 | ||
| نویسندگان | ||
| Saman Rahimirad* 1؛ Mohammad Zarrin2 | ||
| 1Department of Mathematics, Faculty of Science, University of Kurdistan, P.O. Box 416, Sanandaj, Kurdistan, Iran | ||
| 2Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX, 78666, USA | ||
| چکیده | ||
| In this paper we provide some bounds for the probability, denoted by $\mathcal{PC}(G)$, that two randomly chosen elements in a given finite group have the same centralizers. In particular, among other results, we give the following best possible bounds for $\mathcal{PC}(G)$, depending only on $|G:Z(G)|$ and the smallest prime divisor of $|G|$. | ||
| کلیدواژهها | ||
| probability on groups؛ centralizers؛ AC-group | ||
| مراجع | ||
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[1] A. Abdollahi, S. Akbari and H. R. Maimani, Non-commuting graph of a group, J. Algebra, 298 (2006) 468–492. | ||
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