Need help proving homomorphism.
Show that the mapping W:Z6 ->Z24 given by W([B]x/B])=4[B]x/B] is well defined and is in fact a homomorphism. Find the image and kernal of W
Need help proving homomorphism.
Show that the mapping W:Z6 ->Z24 given by W(x)=4x is well defined and is in fact a homomorphism. Find the image and kernal of W
This is well-defined. And .
The kernel are all so that . Which happens when is multiple of , so, .
The image are all so that which happens when .
Note for this equation to be solvable we require to divide . Thus, .