1. ## isomorphism

may i know what does it mean by a group is isomorphic to itself by the identity function?

thanks

2. Hi

It just means that if you consider the identity function $id_G,$ where $(G,.)$ is your group, then:

$id_G\ :\ G\rightarrow G\ :\ x\mapsto x$ is a morphism, that is $id_G(a.b)=id_G(a).id_G(b)$ for all $a,b\in G.$

This assertion is quite trivial, since the equality above means $a.b=a.b,$ which is obviously true.