Isn't it pretty obvious? If homomorphism is supposed to preserve structure, it must map GROUPS onto GROUPS (possibly of a different order, if this homomorphism isn't ISOmorphism), so whatever it maps to in the codomain, it must be its SUBGROUP (proper or not).
@user-fc8xw4fi5v yeah but something being obvious to you doesn't mean that you can prove it easily so it's np (i dont remember wtf im talkin about here tho)
You should use two distinct operators, the one for domain and the one for codomain.
Because you know these two operators can be quite different ones.
Isn't it pretty obvious? If homomorphism is supposed to preserve structure, it must map GROUPS onto GROUPS (possibly of a different order, if this homomorphism isn't ISOmorphism), so whatever it maps to in the codomain, it must be its SUBGROUP (proper or not).
sounds obvious but it is not until u prove it tho. but its easy to prove so no problem.
i would just use the subgroup criterion to prove it tho.
@user-fc8xw4fi5v yeah but something being obvious to you doesn't mean that you can prove it easily so it's np (i dont remember wtf im talkin about here tho)