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9.1 (1984)

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A group $G$ is said to be potent if, to each $x \in G$ and each positive integer $n$ dividing the order of $x$ (we suppose $\infty$ is divisible by every positive integer), there exists a finite homomorphic image of $G$ in which the image of $x$ has order precisely $n$. Is the free product of two potent groups again potent?

Contributor: R. B. J. T. Allenby

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