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13.58 (1995)

Solved

Let $\varphi$ be an automorphism of prime order $p$ of a nilpotent (periodic) group $G$ such that $C_G(\varphi)$ is a group of finite sectional rank $r$. Does $G$ possess a normal subgroup $N$ which is nilpotent of class bounded by a function of $p$ only and is such that $G/N$ is a group of finite sectional rank bounded in terms of $r$ and $p$?

Contributor: E. I. Khukhro

Progress

Yes, it does (E. I. Khukhro, J. London Math. Soc., 77 (2008), 130–148).

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