I know that the group $S_6$ has an outer automorphism. I also know that group theory, specifically the simplicity of $A_5$, implies that quintics are unsolvable. Does the outer automorphism of $S_6$ have easy-to-state consequences in the algebra of rational, real, or complex numbers, like the statement "general quintics are unsolvable"?
2026-04-02 04:41:44.1775104904
What implications does the outer automorphism of $S_6$ have in the algebra of rational, real, or complex numbers?
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