may i know what does it mean by a group is isomorphic to itself by the identity function?
thanks
Hi
It just means that if you consider the identity function $\displaystyle id_G,$ where $\displaystyle (G,.)$ is your group, then:
$\displaystyle id_G\ :\ G\rightarrow G\ :\ x\mapsto x$ is a morphism, that is $\displaystyle id_G(a.b)=id_G(a).id_G(b)$ for all $\displaystyle a,b\in G.$
This assertion is quite trivial, since the equality above means $\displaystyle a.b=a.b,$ which is obviously true.