The Extrinsic Primitive Torsion Problem

Khalid Bou-Rabee, W. Patrick Hooper

Let $P_k$ be the subgroup generated by $k$th powers of primitive elements in $F_r$, the free group of rank $r$. We show that $F_2/P_k$ is finite if and only if $k$ is $1$, $2$, or…