A cautionary tale

This was just reported to me by a group theorist.

He asked ChatGPT whether Aut(G) wr Sym(n) is a subgroup of Aut(G^n). It was honest enough to say that it didn’t know (though it said it in a rather roundabout way).

Then he asked whether equality holds when G is a finite simple group. This time it was more definite; it said No. This seemed to be the result of confusion between the automorphism group and the outer automorphism group, together with some waffle masquerading as a proof.