  We apply a recently demonstrated method for precision spectroscopy on strong
transitions in trapped ions to measure both fine structure components of the
3s-3p transition in 24-Mg+ and 26-Mg+. We deduce absolute frequency reference
data for transition frequencies, isotope shifts and fine structure splittings
that are in particular useful for comparison with quasar absorption spectra,
which test possible space-time variations of the fine structure constant. The
measurement accuracy improves previous literature values, when existing, by
more than two orders of magnitude.
