Suppose 0: G-→ G be a homomorphism of groups. Show that: (i) Kere is normal in G (ii) The mappping o: G/ Ker0 →0(G) defined by þ(gKer0) = 0(g) is an isomorphism of groups.

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Suppose 0: G→ G be a homomorphism of groups. Show that:
(i) Kere is normal in G
(ii) The mappping o: G/ Ker0 →0(G) defined by ø(gKer0) = 0(g) is an isomorphism of groups.
Transcribed Image Text:Suppose 0: G→ G be a homomorphism of groups. Show that: (i) Kere is normal in G (ii) The mappping o: G/ Ker0 →0(G) defined by ø(gKer0) = 0(g) is an isomorphism of groups.
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