Abstract
In this article, we prove a conjecture of J. G. Thompson for the finite simple group 2 D n (q). More precisely, we show that every finite group G with the property Z(G) = 1 and N(G) = N(2 D n (q)) is necessarily isomorphic to 2 D n (q). Note that N(G) is the set of lengths of conjugacy classes of G.
ACKNOWLEDGMENTS
The authors wish to thank the referee for the invaluable comments. The first author would like to thank Shahrekord University for the financial support.
Notes
Communicated by P. Tiep.