# Validity of a result from character theory for finite field.

Corollary $$11.29$$ of the book Character Theory of Finite Groups by I. Martin Isaacs as given:

Corollary $$11.29:$$ Let $$H$$ be a normal subgroup of $$G$$ and $$\zeta\in Irr(G), \xi\in Irr(H)$$, be a constituent of $$\zeta_{H}$$. Then $$\zeta(1)/ \xi(1)$$ divides $$|G:H|.$$

My question is can i say that above corollary is valid over any field or only for $$C?$$ Please suggest. Thanks.

• sorry i will edit... – neelkanth Dec 25 '18 at 18:09
• @MatthewTowers i edit it..... – neelkanth Dec 25 '18 at 18:11
• What is your proof for $\mathbb{C}$ ? – reuns Dec 26 '18 at 20:12
• It is given in book ... – neelkanth Dec 26 '18 at 23:32