Quasirecognition by prime graph of L_n(2^α) for some n and α

چکیده مقاله

Let G be a finite group. The prime graph of 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(L_n(2^α)), where n - 4m+3, 3 + α and α is odd, then G has a unique nonabelian composition factor isomorphic to L_n(2α). We also show that if G is a finite group satisfying |G| = |L_n(2α)| and γ(G) = γ(L_n(2^α)), then G ≅ L_n(2α). As a consequence of our result we give a new proof for a conjecture of W. J. Shi and J. X. Bi for L_n(2^α). Application of this result to the problem of recognition of finite simple groups by the set of element orders are also considered. Specially it is proved that by the above conditions, L_n(2α) is quasirecognizable by spectrum.