  We demonstrate the non-negligible effect of transition magnetic moments on
three-flavor collective oscillations of Majorana neutrinos in the core of
type-II supernovae, within the single-angle approximation. We argue that data
from a galactic supernova in conjunction with terrestrial experiments can
potentially give us clues about the non-zero nature of neutrino transition
magnetic moments if these are Majorana fermions, even if their values are as
small as those predicted by the Standard Model augmented by nonzero neutrino
Majorana masses.
