Let be a group and suppose there exists such that the map is an automorphism of Prove that for all

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- May 22nd 2009, 06:27 AMNonCommAlgAlgebra, Problems For Fun (9)
Let be a group and suppose there exists such that the map is an automorphism of Prove that for all

- May 23rd 2009, 05:28 AMSwlabr
Note that is a homomorphism and so . Also, as it is onto every can be written in this form, for some .

Thus, it is sufficient to prove that .

Now, note that

.

Thus, as required.

I hope that's correct - haven't had a chance to check it properly as my wife is badgering me to go through and eat lunch! - May 23rd 2009, 05:38 AMNonCommAlg