An extension theorem for characters

Abstract

If N N is a normal subgroup of the finite group G G and ψ \psi is an irreducible complex character of N N that is invariant in G G , then ψ \psi is extendible to a character of G G if ( | G : N | , | N | / ψ ( 1 ) ) = 1 (\left | {G:N} \right |,\left | N \right |/\psi (1)) = 1