QUASIRECOGNITION BY THE PRIME GRAPH OF L3 (Q) WHERE 3

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SALEHI AMIRI SEYED SADEGH; KHALILI ASBOEI ALIREZA; IRANMANESH ALI; TEHRANIAN ABOLFAZL

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Journal Paper

Paper Information

Journal: Bulletin of the Iranian Mathematical Society Year:2013 | Volume:39 | Issue:2 Page(s): 289-305

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Title

QUASIRECOGNITION BY THE PRIME GRAPH OF L3 (Q) WHERE 3

Author(s)

SALEHI AMIRI SEYED SADEGH | KHALILI ASBOEI ALIREZA | IRANMANESH ALI | TEHRANIAN ABOLFAZL | Issue Writer Certificate

Keywords

PRIME GRAPH

ELEMENT ORDER

SIMPLE GROUP

LINEAR GROUP

Abstract

Let G be a finite group. We construct the PRIME GRAPH of G, which is denoted by G (G) as follows: the vertex set of this graph is the prime divisors of |G| and two distinct vertices p and qare joined by an edge if and only if G contains an element of orderpq. In this paper, we determine finite groups G with G (G) =G (L3 (q)), 2£q<100 and prove that if q 6¹2, 3, then L3 (q) is quasirecognizable by the PRIME GRAPH, i.e., if G is a finite group with the same PRIME GRAPH as the finite SIMPLE GROUP L3 (q), then G has a unique non-Abelian composition factor isomorphic to L3 (q).As a consequence of our results we prove that the SIMPLE GROUP L3 (4) is recognizable and the SIMPLE GROUPs L3 (7) and L3 (9) are 2-recognizable by the PRIME GRAPH.

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APA: Copy

SALEHI AMIRI, SEYED SADEGH, KHALILI ASBOEI, ALIREZA, IRANMANESH, ALI, & TEHRANIAN, ABOLFAZL. (2013). QUASIRECOGNITION BY THE PRIME GRAPH OF L₃ (Q) WHERE 3Vancouver: Copy

SALEHI AMIRI SEYED SADEGH, KHALILI ASBOEI ALIREZA, IRANMANESH ALI, TEHRANIAN ABOLFAZL. QUASIRECOGNITION BY THE PRIME GRAPH OF L₃ (Q) WHERE 3IEEE: Copy

SEYED SADEGH SALEHI AMIRI, ALIREZA KHALILI ASBOEI, ALI IRANMANESH, and ABOLFAZL TEHRANIAN, “QUASIRECOGNITION BY THE PRIME GRAPH OF L₃ (Q) WHERE 3

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