Representação de Grupos – Exercício 2
Assume that G is a finite group, say G = {g1, . . . , gn}, and write c for the element $$\sum_{i=1}^{n}g_{i}$$, of $$\mathbb{C}G$$...
Representação de Grupos
Representação de Grupos – Exercício 1
Seja ρ uma representação de grau 1 de G. Prove que G/Ker(ρ) é abeliano. Suppose that ρ is a representation of G of degree 1. Prove...
Group Representation – Exercise 1
Suppose that ρ is a representation of G of degree 1. Prove that G\Ker(ρ) is abelian. Solution: For $$g,h\in G$$, $$\rho(ghg^{-1}h^{-1})=\rho(g)\rho(h)\phi(g^{-1})\rho(h^{-1}) (*)$$. Since ρ is of...