Let be a homomorphism. Prove that kernel of is infinite.
If is a finite subgroup then all must have norm , i.e. . ( Otherwise otherwise is an infinite sequence of distinct elements in . )
Suppose , that is finite and is the kernel of . Then let and
So, . But this is a contradiction since .
Hence, no finite subgroup of can be a kernel.
Note: The homomorphisms that can easily be described are for the form .