301.10D Properties of Homomorphisms, Image, Kernel

GIving up bijection doesn't mean giving up hope. Homomorphisms, like isomorphisms, also send identity to identity, powers to powers, and inverses to inverses. BUT, we also show that the image of a homomorphism is a SUBGROUP of its target group, and — most importantly of all! — the kernel of a homomorphism is a NORMAL SUBGROUP of its domain group

[PunmasterSTP]

Homomorphisms? More like "Helpful videos; thanks for all of 'em!" 🙏

[sayanjitb]

Why are you coming to the properties of group homomorphism from the notion of isomorphism? Shouldn't it be another way around? Since generally we go to the notion of isomorphism from the notion of homomorphism.
Thanks

[stapleman]

Isomorphism property chart came from video 301.6E