@article {
author = {Salehi Amiri, S. S. and Khalili Asboei, A. and Iranmanesh, A. and Tehranian, A.},
title = {Quasirecognition by the prime graph of L_3(q) where 3 < q < 100},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {39},
number = {2},
pages = {289-305},
year = {2013},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {Let $G$ be a finite group. We construct the prime graph of $ G $,which is denoted by $ Gamma(G) $ as follows: the vertex set of thisgraph is the prime divisors of $ |G| $ and two distinct vertices $ p$ and $ q $ are joined by an edge if and only if $ G $ contains anelement of order $ pq $.In this paper, we determine finite groups $ G $ with $ Gamma(G) =Gamma(L_3(q)) $, $2 leq q < 100 $ and prove that if $ q neq 2, 3$, then $L_3(q) $ is quasirecognizable by prime graph, i.e., if $G$is a finite group with the same prime graph as the finite simplegroup $L_3(q)$, then $G$ has a unique non-Abelian composition factorisomorphic to $L_3(q)$. As a consequence of our results we provethat the simple group $L_{3}(4)$ is recognizable and the simplegroups $L_{3}(7)$ and $L_{3}(9)$ are $2-$recognizable by the primegraph.},
keywords = {Prime graph,element order,simple group,linear group},
url = {http://bims.iranjournals.ir/article_414.html},
eprint = {http://bims.iranjournals.ir/article_414_abb286fd32fe231f0647dce9cdb1cae2.pdf}
}