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20.8 (2022)

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Suppose $K < H < F$ are free groups of finite rank such that $\text{rank}(H) < \text{rank}(K)$, but all proper subgroups of $H$ which contain $K$ have ranks $\geqslant \text{rank}(K)$. Then is the inclusion of $H$ in $F$ the only homomorphism $H \to F$ fixing all elements of $K$?

Contributor: G. M. Bergman

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