For any group G, GIZ(G) is isomorphic to Inn(G)
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For any group G, GIZ(G) is isomorphic to Inn(G)
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- 18. If is a subgroup of the group such that for all left cosets and of in, prove that is normal in.Suppose that is an epimorphism from the group G to the group G. Prove that is an isomorphism if and only if ker =e, where e denotes the identity in G.24. Let be a cyclic group. Prove that for every normal subgroup of , is a cyclic group.