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  1. #1
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    isomorphic

    how do i prove that if the centre of a group G is trivial then inn G is isomorphic to G.

    can i say that if the centre of the group G is trival, then the quotient is G itself.
    using the fact G/ centre is iso to InnG, we conclude that G is iso to inn G
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  2. #2
    Senior Member Tinyboss's Avatar
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    Yes, that's right. Show that there's a homomorphism from G onto Inn(G) (given by conjugation), then that the kernel of this map is the center of G. Then use first isomorphism.
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