ON COMPOSITION FACTORS OF A GROUP WITH THE SAME PRIME GRAPH AS Ln(5)

Document Type : Original Manuscript

Author

Department of Mathematics, Tehran North Branch, Islamic Azad University, Tehran, IRAN.

Abstract

The prime graph of a finite group

G

is denoted by

g a (G)

. A nonabelian simple group

G

is called quasirecognizable by prime
graph, if for every finite group

H

, where

g a (H) = g a (G)

, there
exists a nonabelian composition factor of

H

which is isomorphic to

G

. Until now, it is proved that some finite linear simple groups are
quasirecognizable by prime graph, for instance, the linear groups

L_{n} (2)

and

L_{n} (3)

are quasirecognizable by prime graph. In this paper, we consider the
quasirecognition by prime graph of the simple group

L_{n} (5)

Keywords