On the conjectures of J. Thompson and O. Ore

Ellers, Erich; Gordeev, Nikolai

doi:10.1090/S0002-9947-98-01953-9

On the conjectures of J. Thompson and O. Ore
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by Erich W. Ellers and Nikolai Gordeev PDF

Trans. Amer. Math. Soc. 350 (1998), 3657-3671 Request permission

Abstract:

If $G$ is a finite simple group of Lie type over a field containing more than $8$ elements (for twisted groups $^{l} X_{n} (q^{l})$ we require $q > 8$, 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 $G$ is the square of some conjugacy class and consequently every element in $G$ is a commutator.

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