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On the conjectures of J. Thompson and O. Ore

Author(s): Erich W. Ellers; Nikolai Gordeev
Journal: Trans. Amer. Math. Soc. 350 (1998), 3657-3671.
MSC (1991): Primary 20G15
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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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Additional Information:

Erich W. Ellers
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
Email: ellers@math.utoronto.ca

Nikolai Gordeev
Affiliation: Department of Mathematics, Russian State Pedagogical University, Moijka 48, St. Petersburg, Russia 191-186
Email: algebra@ivt.rgpu.spb.ru

DOI: 10.1090/S0002-9947-98-01953-9
PII: S 0002-9947(98)01953-9
Received by editor(s): April 5, 1996
Received by editor(s) in revised form: October 10, 1996
Additional Notes: Research supported in part by NATO collaborative research grant CRG 950689
Copyright of article: Copyright 1998, American Mathematical Society

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M. Herzog, Covering numbers for groups, Groups St. Andrews 1997 in Bath. (Bath, UK, July 26 - August 9, 1997), Lond. Math. Soc. Lect. Note Ser., vol. 260, Cambridge University Press, Cambridge, UK, 1999, pp. 353 - 355. (English)

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