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Primitive elements in a free group with trivial projection

For a free group $F$, an element $w$ is primitive if it is part of some free basis for $F$. Let $\pi:F[x_0,x_1,...,x_n]\rightarrow F[x_1,x_2,...,x_n]$ be defined $\pi (x_0)=1$ and $\pi (x_i)=x_i$ for …
Andrew Clifford's user avatar