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The fully relativistic theory of the Zeeman splitting of the $1s$ hyperfinestructure levels in hydrogenlike ions is considered for the magnetic fieldmagnitude in the range from 1 to 10 T. The second-order corrections to theBreit -- Rabi formula are calculated and discussed. The results can be used fora precise determination of nuclear magnetic moments from $g$ factorexperiments.Comment: 13 page

Zeeman effect of the hyperfine-structure levels in hydrogenlike ions