  We construct a CAT(0) group containing a finitely presented subgroup with
infinitely many conjugacy classes of finite-order elements. Unlike previous
examples (which were based on right-angled Artin groups) our ambient CAT(0)
group does not contain any rank 3 free abelian subgroups.
  We also construct examples of groups of type F_n inside mapping class groups,
Aut(F), and Out(F) which have infinitely many conjugacy classes of finite-order
elements.
