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On the conjectures of J. Thompson and O. Ore

Authors:	Erich W Ellers Nikolai Gordeev

Institution:	Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3 ; Department of Mathematics, Russian State Pedagogical University, Moijka 48, St. Petersburg, Russia 191-186

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

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