2

Let $G$ be a finite group into the field $\mathbb{C}$, then the number of irreducible characters of $G$ is equal to the number of conjugacy classes of $G$, and there is the relationship

$$|G|=\sum_{1\le i\le k}n_i^2$$ where $k$ is the number of irreducible representation of $G$.

Result: The degrees of the irreducible characters are divisors of the order of $G$.

I thought that with the facts above I can prove this result, but I couldn't, This result seems trivial (I can be wrong), can someone help me?

Mrcrg
  • 2,969
  • 7
    This is anything but a trivial result. The standard proof of this fact uses the theory of algebraic integers and requires a few non trivial lemmas. You can also try to read about this here: https://math.stackexchange.com/questions/243221/proofs-that-the-degree-of-an-irrep-divides-the-order-of-a-group – Mark Jul 23 '20 at 00:05

0 Answers0