The probability that two elements of a group have the same centralizers

Rahimirad, Saman; Zarrin, Mohammad

doi:10.22108/ijgt.2024.142171.1912

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	The probability that two elements of a group have the same centralizers
International Journal of Group Theory
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 09 مهر 1403 اصل مقاله (420.34 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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The probability that two elements of a group have the same centralizers