Finite groups whose non-linear irreducible characters of the same degree   are Galois conjugate
  We classify the finite groups whose non-linear irreducible characters that are not conjugate under the natural Galois action have distinct degrees, therefore extending the results in Berkovich et al. [Proc. Amer. Math. Soc. {\bf 115} (1992), 955-959] and Dolfi et al. [Israel J. Math. {\bf 198} (2013), 283-331]. 
Silvio Dolfi and Manoj K. Yadav
math.GR