Abstract
In this paper, we prove a conjecture of Thompson for an infinite class of simple groups of Lie type. In fact, we show that every finite group G with the property Φ(G) ∩ Z(G) = 1 and N(G) = N(Dn(q)) is isomorphic to Z(G) × Dn(q), where n ≥ 5 and n ≠ 8. Note that N(G), Φ(G) and Z(G) are the set of lengths of conjugacy classes of G, Frattini subgroup of G and the center of G, respectively.
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