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9.21 (1984)

Solved

Let $P$ be a maximal parabolic subgroup of the smallest index in a finite group $G$ of Lie type $E_6, E_7, E_8$, or ${}^2E_6$ and let $X$ be a subgroup such that $PX = G$. Is it true that $X = G$?

Contributor: V. D. Mazurov

Progress

Yes, it is true (mod CFSG) (C. Hering, M. W. Liebeck, J. Saxl, J. Algebra, 106, no. 2 (1987), 517–527).

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