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

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- January 24th 2011, 10:56 PMthanhutheHelp about rep group!
Let G be an nonabelian has oder of 8. Let x be a character. Show that x(1)=1

- January 25th 2011, 12:48 AMtonio
- January 25th 2011, 02:44 AMTheArtofSymmetry
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, can be a matrix representation (verify this), which maps the identity of to identity matrix in , i.e., , where is the character of . - February 16th 2011, 05:18 AMthanhuthe
Thanks so much!