isomorphism

Aug 2009
639
2
may i know what does it mean by a group is isomorphic to itself by the identity function?

thanks
 
Nov 2008
354
185
Paris
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.
 
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