# Nessary and sufficient condition for homomorphism to be isomorphism.

1. Sep 9, 2011

### AAQIB IQBAL

The necessary and sufficient condition for homomorphisim f of a group G into a group G' with kernel K to be isomorphism of G into G' is that k={e}
.... THOUGH I AM ABLE TO PROVE THAT f IS ONE-ONE AND f IS HOMOMORPHISM (in converse part) BUT CAN'T GET ANY IDEA TO PROVE THAT f IS ONTO.