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18.67 (2014)

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Suppose that a finite group $G$ admits a Frobenius group of automorphisms $FH$ with kernel $F$ and complement $H$ such that $C_G(F) = 1$. Is the exponent of $G$ bounded in terms of $|F|$ and the exponent of $C_G(H)$?

Contributor: N. Yu. Makarenko, E. I. Khukhro, P. Shumyatsky

Progress

This was proved when $F$ is cyclic (E. I. Khukhro, N. Y. Makarenko, P. Shumyatsky, Forum Math., 26 (2014), 73–112) and for $FH \cong A_4$ when $(|G|, 3) = 1$ (P. Shumyatsky, J. Algebra, 331 (2011), 482–489).

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