Let and be any two groups, and let x be given by . Prove that f is a homomorphism of groups and give ker f.

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- April 20th 2009, 08:36 PMfunnyingaKernels and homomorphism of groups
Let and be any two groups, and let x be given by . Prove that f is a homomorphism of groups and give ker f.

- April 20th 2009, 09:06 PMGamma
we show it is a homomorphism.

Let

- April 20th 2009, 09:09 PMTheEmptySet
- April 20th 2009, 09:29 PMGammaGeneralization
I was just thinking it might be of interest to you to note that this same concept can be generalized to multiple products and considering the mapping by

This is a homomorphism and the kernel of this is . And if you apply the first isomorphism theorem you know that