Let p be any prime. P n a Sylow -subgroup of the symmetric group S . ϕ and ψ linear characters let N normaliser in In this article we show that inductions to are equal if, only –conjugate. This is an analogue for groups result Navarro -solvable groups.

In this paper, we study the structure of nite Frobenius groups whose non-rational or non-real irreducible characters are linear.

In previous work (Dawsey et al. in J Algebra 533:339–343, 2019), the authors confirmed speculation of J.G. Thompson that certain multiquadratic fields are generated by specified character values sufficiently large alternating groups $$A_n$$ . Here we address natural generalization this to finite general linear $$\mathrm {GL}_m\left( {{\mathbb {F}}}_q\right) $$ and {SL}_2\left(