Yazd University Algebraic Structures and Their Applications 2382-9761 9 2 2022 08 09 A new characterization of Projective Special Unitary groups $\mathbf{ U_3 (3^n )}$ by the order of group and the number of elements with the same order 113 120 2675 10.22034/as.2022.2675 EN Behnam Ebrahimzadeh Department of Mathematics, Persian Gulf University, Bushehr, Iran 0000-0001-5696-275x Ali Iranmanesh Department of Mathematics, Tarbiat Modares University, Tehran, Iran 0000-0003-2639-9454 Journal Article 2021 09 22 In this paper, we prove that projective special unitary groups $U_3 (3^n)$, where $ 3^{2n}-3^{n}+1$ is a prime number and $3^n\equiv\pm2(\mod 5)$, can be uniquely determined by the order of group and the number of elements with the same order. https://as.yazd.ac.ir/article_2675_609f365e23655404c49e8672ef7ade41.pdf