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18.1 (2014)

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Given a group $G$ of finite order $n$, does there necessarily exist a bijection $f$ from $G$ onto a cyclic group of order $n$ such that for each element $x \in G$, the order of $x$ divides the order of $f(x)$?

Contributor: I. M. Isaacs

Progress

An affirmative answer in the case where $G$ is solvable was given by F. Ladisch.

*Yes, it does (M. Amiri, J. Pure Applied Algebra, 228, no. 7 (2024), 107632).

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