Thread: Help about rep group!

Let G be an nonabelian has oder of 8. Let x be a character. Show that x(1)=1

Originally Posted by thanhuthe

Let G be an nonabelian has oder of 8. Let x be a character. Show that x(1)=1

A character is always a group homomorphism, so...

Tonio

Ps. By the way, the above is true for ANY group, not only non-abelian ones of order 8.

Do you mean a multiplicative character (linear character) or a character of a representation? If you are referring the latter, it is not always true that x(1)=1.

For example, _8 \rightarrow GL_2(\mathbb{Re})" alt="\phi_8 \rightarrow GL_2(\mathbb{Re})" /> can be a matrix representation (verify this), which maps the identity of to identity matrix in , i.e., , where is the character of .

Thanks so much!