Is it true that, given any free group $F$ and any set $S\subseteq F$ which generates $F$, there is a subset $T\subseteq S$ which is a free generating set for $F$?
It would be great if you could give me some literature recommendations.
2026-03-28 10:41:42.1774694502
subsets of a generating set of a free group
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Notice that $\{2,3\}$ is a generator set of the free group $\mathbb{Z}$, but no proper subset generates the group.