Nearly Rational Frobenius Groups

Throughout this paper all groups are finite. A group in which all irreducible characters are rational is called rational group. In [4], Darafsheh and Sharifi characterize all rational Frobenius groups. In [9], Norooz-Abadian and Sharifi find the structure of Frobenius Q′ 1-groups, that is, non-rational Frobenius groups whose non-rational irreducible characters are linear. In this paper, we provide a different short proof of the following theorem