About the splitting field for rational valued characters

  • Ion Armeanu


The problem of finding the splitting field for group characters is very old and important (see [4], Chapter 9). The most part of the papers on this subject are concerned with all irreducible characters of a group under certain conditions. It seems more difficult to obtain minimal splitting fields for only one character without strong conditions about the group. In this case, naturally,the number theoretical methods play an essential role. This paper concerns to prove that under certain circumstances if a rational character of a group has Q(21/2,i) as splitting field, then Q(i) or even Q(21/2) are splitting fields too.