Orthogonal irreducible representations of finite solvable groups in odd dimension.

We prove that if G$G$ is a finite irreducible solvable subgroup of an orthogonal group O(V,Q)$O(V,Q)$ with dimV$\dim V$ odd, then G$G$ preserves an orthogonal decomposition of V$V$ into 1‐spaces. In particular G$G$ is monomial. This generalizes a theorem of Rod Gow. [ABSTRACT FROM AUTHOR]