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| Paper IPM / M / 11468 |
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| Abstract: | |
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The prime graph of a finite group G is denoted by Γ(G). In this paper as the main result, we show that if G is a finite group such that Γ(G) = Γ(F4(q)), where q=2n > 2, then G has a unique nonabelian composition factor isomorphic to F4(q).We also show that if G is a finite group satisfying |G| = |F4(q)| and Γ(G) = Γ(F4(q)), where q = 2n > 2, then G ≅ F4(q). As a consequence of our result we give a new proof for a conjecture of Shi and Bi for F4(q) where q = 2n > 2.
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