In the article "Automorphism groups of simple algebras and group algebras" (1978), Janusz conjectures the following:



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> The group algebra $\mathbb{Q} G$ for a non-trivial finite group has an outer automorphism (=non-inner automorphism)?
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> Question: Is this conjecture solved ?
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Do rational group algebras have an outer automorphism?
This conjecture was proved in Feit, Walter; Seitz, Gary M.
On finite rational groups and related topics.
Illinois J. Math. 33 (1989), no. 1, 103–131. The proof relies on the classification since this easily reduces to the case of simple groups.


