The contribution of core nucleons to a static magnetic quadrupole mome
nt is calculated in the presence of an interaction that violates P and
T invariance. The contribution found can be comparable or even larger
than the contribution of a valence nucleon, in contrast to the case o
f the P-violating but T-invariant anapole moment. The core contributio
n appears to be sensitive to the spin-orbit single-particle potential,
which enhances it by a factor of similar to 2.