The anomalous magnetic moment of the electron in hydrogenlike ions

The precise determination of the anomalous magnetic moment of the electron bound in hydrogen-like ions allows for a stringent test of quantum electrodynamics (QED) in the presence of strong electric fields. g-factor measurements on the electron bound in hydrogen-like ions C-12(5+) and O-16(7+), using single ions confined in a Penning trap, have yielded values in agreement with theory on the ppb level. If the QED calculations are considered correct, the results can in turn be used for a determination of fundamental constants like the electron mass me, the. ne structure constant a or nuclear parameters. We report about present developments towards g-factor measurements also in medium-heavy and heavy highly-charged ions.