On the Validity of Thompson's Conjecture for Finite Simple Groups

摘要

In this article, we prove a conjecture of J. G. Thompson for the finite simple group ~2D_n(q). More precisely, we show that every finite group G with the property Z(G) = 1 and N(G) = N(~2D_n(q)) is necessarily isomorphic to ~2D_n(q). Note that N(G) is the set of lengths of conjugacy classes of G.