University of Isfahan International Journal of Group Theory 2251-7650 1 3 2012 09 01 Quasirecognition by prime graph of U3(q) where 2 < q = pα < 100 51 66 1369 10.22108/ijgt.2012.1369 EN Seyed Sadegh Salehi Amiri Islamic Azad University Alireza Khalili Asboei Islamic Azad University Ali Iranmanesh Tarbiat Modares University Abolfazl Tehranian Islamic Azad University Journal Article 2012 03 09 Let $G $ be a finite group and let $\Gamma(G)$ be the prime graph‎ ‎of G‎. ‎Assume $2 < q = p^{\alpha} < 100$‎. ‎We determine finite groups‎ ‎G such that $\Gamma(G) = \Gamma(U_3(q))$ and prove that if $q \neq‎ ‎3‎, ‎5‎, ‎9‎, ‎17$‎, ‎then $U_3(q)$ is quasirecognizable by prime graph‎, ‎i.e‎. ‎if $G$ is a finite group with the same prime graph as the‎ ‎finite simple group $U_3(q)$‎, ‎then $G$ has a unique non-Abelian‎ ‎composition factor isomorphic to $U_3(q)$‎. ‎As a consequence of our‎ ‎results‎, ‎we prove that the simple groups $U_{3}(8)$ and $U_{3}(11)$‎ ‎are $4-$recognizable and $2-$recognizable by prime graph‎, ‎respectively‎. ‎In fact‎, ‎the group $U_{3}(8)$ is the first example‎ ‎which is a $4-$recognizable by prime graph‎. https://ijgt.ui.ac.ir/article_1369_3a2c5d4f00b6ca4392b6fc4dafbcde67.pdf