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17.71 (2010)

Partially Solved

Let $\alpha$ be a fixed-point-free automorphism of prime order $p$ of a periodic group $G$.
$\qquad$ a) Is it true that $G$ does not contain a non-trivial $p$-element?
$\qquad$ b) Suppose that $G$ does not contain a non-trivial $p$-element. Is $\alpha$ a splitting automorphism?

Contributor: V. D. Mazurov

Progress

a) No, it may contain a non-trivial $p$-element (E. B. Durakov, A. I. Sozutov, Algebra Logic, 52, no. 5 (2013), 422–425).

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