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| Paper IPM / M / 8548 |
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| Abstract: | |
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Let G be a finite group. The main result of this paper is as
follows: If G is a finite group, such that Γ(G) = Γ(2G2(q)), where q = 32n+1 for some n ≥ 1,
then G has a (unique) nonabelian composition factor isomorphic
to 2G2(q). As a consequence, we prove that if G is a
finite group satisfying |G| = |2G2(q)| and Γ(G) = Γ(2G2(q)) then G ≅ 2G2(q). This enables us
to give new proofs for some theorems; e.g., a conjecture of W. Shi
and J. Bi. Applications of this result are also considered to the
problem of recognition by element orders of finite groups.
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