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Set of all Inner Automorphisms of a Group

Modern Algebra
Group Theory (LXXII)
The Set of all Automorphisms of a Group
The Set of all Inner Automorphisms of a Group

Prove that if G be a group and Z(G), the centre of G, then G/Z(G) is equivalent to I(G), where I(G) is the set of all inner automorphisms of G.

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Solution Summary

It is proven that if G be a group and Z(G), the centre of G, then G/Z(G) is equivalent to I(G), where I(G) is the set of all inner automorphisms of G. The solution is detailed and well presented.

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