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14.1 (1999)

Solved

Suppose that $G$ is a finite group with no non-trivial normal subgroups of odd order, and $\varphi$ is its $2$-automorphism centralizing a Sylow $2$-subgroup of $G$. Is it true that $\varphi^2$ is an inner automorphism of $G$?

Contributor: R. Zh. Aleev

Progress

Yes, it is true (G. Glauberman, Math. Z., 107 (1968), 1–20).

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