It is possible to show easily that is isomorphic with the group of units denoted that have a multiplicative inverse modulo 3 .
defined by the isomorphic map :
Furthermore we can find another isomorphic map to show that
I cannot really prove that the map cannot be an isomorphism. However i can define the map and by counter-example to prove that this is not isomorphic as
if it is an isomorphism
but which does equal 3
However this is not very rigorous and I would like to know if there a deeper/more rigorous way of proving that there cannot be an isomorphism