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7.15 (1980)

Open

Prove that if $F^*(G)$ is quasisimple and $\alpha \in \operatorname{Aut} G$, $|\alpha| = 2$, then $C_G(\alpha)$ contains an involution outside $Z(F^*(G))$, except when $F^*(G)$ has quaternion Sylow 2-subgroups.

Contributor: R. Griess

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