Group representation

Representations of finite groups

In general, a representation of a finite group with a finite carrier space is a homomorphism , i.e. representation matrices of finite group elements have determinant 1. rep

Proof

Let be a finite group and be a representation thereof with finite carrier space. Assume there exists such that . Then for all , and therefore for all . Thus the cyclic subgroup is infinite, contradicting our requirement. Therefore for all

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