If g is an abelian group and phi: g rightarrow g' is a homomorphism of g onto g', prove that g' is abelian.

If is a homomorphism, then we have, for every

Since G is abelian, we have , and thus

But we also have

which proves that G' is abelian.

In other words, for every , you have , because there exist such that , and you can think of as , and of and

Then, you observe that because they mean , and by hypothesis, because G is abelian.

beanburito

step-by-step explanation: