@article {
author = {Salehi Amiri, Seyed Sadegh and Khalili Asboei, Alireza and Iranmanesh, Ali and Tehranian, Abolfazl},
title = {Quasirecognition by prime graph of U_{3}(q) where 2 < q = p^{α} < 100},
journal = {International Journal of Group Theory},
volume = {1},
number = {3},
pages = {51-66},
year = {2012},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2012.1369},
abstract = {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.},
keywords = {prime graph,Element order,simple group,linear group},
url = {https://ijgt.ui.ac.ir/article_1369.html},
eprint = {https://ijgt.ui.ac.ir/article_1369_3a2c5d4f00b6ca4392b6fc4dafbcde67.pdf}
}