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11.13 (1990)

Solved

Suppose that $G$ is a periodic group with an involution $i$ such that $i^g \cdot i$ has odd order for any $g \in G$. Is it true that the image of $i$ in $G/O(G)$ belongs to the centre of $G/O(G)$?

Contributor: A. V. Borovik

Progress

No, not always (E. B. Durakov, A. I. Sozutov, Algebra Logic, 52, no. 5 (2013), 422–425).

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