  The knot concordance group can be contextualized as organizing problems about
3- and 4-dimensional spaces and the relationships between them. Every
3-manifold is surgery on some link, not necessarily a knot, and thus it is
natural to ask about such a group for links. In 1988, Le Dimet constructed the
string link concordance groups and in 1998, Habegger and Lin precisely
characterized these groups as quotients of the link concordance sets using a
group action. Notably, the knot concordance group is abelian while, for each
$n$, the string link concordance group on $n$ strands is non-abelian as it
contains the pure braid group on $n$ strands as a subgroup. In this work, we
prove that even the quotient of each string link concordance group by its pure
braid subgroup is non-abelian.
