TY - JOUR
ID - 414
TI - Quasirecognition by the prime graph of L_3(q) where 3 < q < 100
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Salehi Amiri, S. S.
AU - Khalili Asboei, A. R.
AU - Iranmanesh, A.
AU - Tehranian, A.
AD - Islamic Azad University
AD - Tarbiat Modares University
Y1 - 2013
PY - 2013
VL - 39
IS - 2
SP - 289
EP - 305
KW - Prime graph
KW - element order
KW - simple group
KW - linear group
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_414.html
L1 - http://bims.iranjournals.ir/article_414_abb286fd32fe231f0647dce9cdb1cae2.pdf
ER -