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

In this article, we prove a conjecture of J. G. Thompson for the finite simple group2Dn(q). More precisely, we show that every finite groupGwith the propertyZ(G) = 1 andN(G) = N(2Dn(q)) is necessarily isomorphic to2Dn(q). Note thatN(G) is the set of lengths of conjugacy classes ofG. [ABSTRACT FROM PUBLISHER]