Abstract
Abstract Let 𝐺 be a finite group and let Irr s ( G ) \mathrm{Irr}_{\mathfrak{s}}(G) be the set of irreducible complex characters 𝜒 of 𝐺 such that χ ( 1 ) 2 \chi(1)^{2} does not divide the index of the kernel of 𝜒. In this paper, we classify the finite groups 𝐺 for which any two characters in Irr s ( G ) \mathrm{Irr}_{\mathfrak{s}}(G) are Galois conjugate. In particular, we show that such groups are solvable with Fitting height 2.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have