%0 Journal Article
%T Quasirecognition by the prime graph of L_3(q) where 3 < q < 100
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Salehi Amiri, S. S.
%A Khalili Asboei, A. R.
%A Iranmanesh, A.
%A Tehranian, A.
%D 2013
%\ 05/01/2013
%V 39
%N 2
%P 289-305
%! Quasirecognition by the prime graph of L_3(q) where 3 < q < 100
%K Prime graph
%K element order
%K simple group
%K linear group
%R
%X 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.
%U http://bims.iranjournals.ir/article_414_abb286fd32fe231f0647dce9cdb1cae2.pdf