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17.70 (2010)

Open

Let $\alpha$ be an automorphism of prime order $q$ of an infinite free Burnside group $G = B(q, p)$ of prime exponent $p$ such that $\alpha$ cyclically permutes the free generators of $G$. Is it true that $\alpha$ fixes some non-trivial element of $G$?

Contributor: V. D. Mazurov

Progress

Editors’ comment: this is proved for $q = 2$ in (V. S. Atabekyan, H. T. Aslanyan, Proc. Yerevan State Univ. Physic. Math. Sci., 53, no. 3 (2019), 147–149).

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