“…Given a peripheral subgroup
and a single element
that is disjoint from every conjugate of
, it is straightforward to find a finite quotient that witnesses this disjointness [
18, Lemma 4.5]. Given non‐conjugate subgroups
and
, Chagas and Zalesskii find a finite quotient of
where their images are not conjugate [
4]. Given a pair of non‐conjugate peripheral subgroups
and
, Wilton and Zalesskii use an argument of Hamilton to construct a finite quotient
, such that non‐trivial elements of
and
always lie in distinct conjugacy classes [
31, Lemma 4.6].…”