  Brou\'e, Malle and Rouquier conjectured in that the center of the pure braid
group of an irreducible finite complex reflection group is cyclic. We prove
this conjecture, for the remaining exceptional types, using the analogous
result for the full braid group due to Bessis, and we actually prove the
stronger statement that any finite index subgroup of such braid group has
cyclic center.
