Resumen de Degree homogeneous subgroups
John D. Dixon, A. Rahnamai Barghi
Let G be a finite group and H be a subgroup. We say that H is degree homogeneous if, for each chi \in Irr(G), all the irreducible constituents of the restriction chiH have the same degree. Subgroups which are either normal or abelian are obvious examples of degree homogeneous subgroups. Following a question by E. M. Zhmud we investigate general properties of such subgroups. It appears unlikely that degree homogeneous subgroups can be characterized entirely by abstract group properties, but we provide mixed criteria (involving both group structure and character properties) which are both necessary and sufficient. For example, H is degree homogeneous in G if and only if the derived subgroup H' is normal in G and, for every pair alpha, beta of irreducible G-conjugate characters of H', all irreducible constituents of alphaH and betaH have the same degree.
