Paper Information

Journal:   INTERNATIONAL JOURNAL OF GROUP THEORY   SEPTEMBER 2012 , Volume 1 , Number 3; Page(s) 51 To 66.
 
Paper: 

QUASIRECOGNITION BY PRIME GRAPH OF U3(Q) WHERE WHERE 2 < Q= Pα<100

 
 
Author(s):  SALEHI AMIRI SEYED SADEGH*, KHALILI ASBOEI ALIREZA, IRANMANESH ALI, TEHRANIAN ABOLFAZL
 
* DEPARTMENT OF MATHEMATICS, SCIENCE AND RESEARCH BRANCH, ISLAMIC AZAD UNIVERSITY, TEHRAN, IRAN
 
Abstract: 
Let G be a nite group and let G(G) be the prime graph of G. Assume 2<q=pa< 100.
We determine finite groups G such that
G (G) =G (U3 (q)) and prove that if q¹3; 5; 9; 17, then U3 (q) is quasirecognizable by prime graph, i.e. if G is a finite group with the same prime graph as the finite simple group U3 (q), then G has a unique non-Abelian composition factor isomorphic to U3 (q). As a consequence of our results, we prove that the simple groups U3 (8) and U3 (11) are 4-recognizable and 2-recognizable by prime graph, respectively. In fact, the group U3 (8) is the rst example which is a 4-recognizable by prime graph.
 
Keyword(s): PRIME GRAPH, ELEMENT ORDER, SIMPLE GROUP, LINEAR GROUP
 
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