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18.82 (2014)

Solved

Is there a function $f : \mathbb{N} \to \mathbb{N}$ such that for any prime $p$, if $p^{f(n)}$ divides the order of a finite group $G$, then $p^n$ divides the order of $\text{Aut } G$?

Contributor: R. M. Patne

Progress

Yes, there is. This was established in (J. A. Green, Proc. Roy. Soc. London Ser. A., 237 (1956), 574–581), which improved a previous result with a function depending on $p$ in (W. Ledermann, B. H. Neumann, Proc. Roy. Soc. London. Ser. A, 235 (1956), 235–246).

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