Coprime-degree determinant extension theorem
= Coprime-degree determinant extension theorem
Suppose $N\triangleleft G$, $G/N$ is solvable, $\theta\in\operatorname{Irr}(N)$ is invariant under $G$, and $\theta(1)$ is coprime to $[G:N]$. If a <linear character> $\mu$ of $G$ restricts to the <determinant character> $\det\theta$, then there is a unique <character extension> $\chi\in\operatorname{Irr}(G)$ with determinant $\mu$. This is the solvable-quotient extension result supplied for the exam's application.