On the conjectures of J. Thompson and O. Ore

Abstract

If G G is a finite simple group of Lie type over a field containing more than 8 8 elements (for twisted groups l X n ( q l ) ^{l} X_{n} (q^{l}) we require q > 8 q > 8 , except for 2 B 2 ( q 2 ) ^{2} B_{2} (q^{2}) , 2 G 2 ( q 2 ) ^{2} G_{2} (q^{2}) , and 2 F 4 ( q 2 ) ^{2} F_{4} (q^{2}) , where we assume q 2 > 8 q^{2} > 8 ), then G G is the square of some conjugacy class and consequently every element in G G is a commutator.