University of Isfahan International Journal of Group Theory 2251-7650 15 1 2025 03 12 The clique number of the intersection graph of some cyclic groups 9 16 29354 10.22108/ijgt.2025.140733.1892 EN Arezoo Beheshtipour Department of Mathematics, University of Zanjan, P.O. Box 45371-38791, Zanjan, Iran Seyyed Majid Jafarian Amiri Department of Mathematics, University of Zanjan, P.O. Box 45371-38791, Zanjan, Iran Journal Article 2024 02 17 For a nontrivial finite group $G$, the intersection graph $\Gamma(G)$ of $G$ is a simple undirected graph whose vertices are the nontrivial proper subgroups of $G$ and two vertices are joined by an edge if and only if they have a nontrivial intersection. In this paper, we obtain the clique number of the intersection graph of cyclic groups whose orders have four prime divisors. Moreover we find the clique number of the intersection graph of cyclic groups of order $n$ such that all powers of prime divisors of $n$ are equal. As a special case, we find the clique number of this graph for the cyclic groups of the square-free orders. https://ijgt.ui.ac.ir/article_29354_958cd70935c3a2f6172a70af74126881.pdf