University of Isfahan International Journal of Group Theory 2251-7650 14 4 2024 11 11 The probability that two elements of a group have the same centralizers 223 233 28770 10.22108/ijgt.2024.142171.1912 EN Saman Rahimirad Department of Mathematics, Faculty of Science, University of Kurdistan, P.O. Box 416, Sanandaj, Kurdistan, Iran Mohammad Zarrin Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX, 78666, USA Journal Article 2024 07 27 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 $|G|$. https://ijgt.ui.ac.ir/article_28770_919c859c8fe7d80fc09eef9e7eda022a.pdf