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17.127 (2010)

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Suppose that a finite soluble group $G$ of derived length $d$ admits an elementary abelian $p$-group of automorphisms $A$ of order $p^n$ such that $C_G(A) = 1$. Must $G$ have a normal series of $n$-bounded length with nilpotent factors of $(p, n, d)$-bounded nilpotency class?

An affirmative answer would follow from an affirmative answer to 11.125.

Contributor: P. Shumyatsky

Progress

This is true for $p = 2$.

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