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.

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

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