How do I prove that all characteristic subgroups $H\subset G$ are normal? I tried to prove that $gHg^{-1}\subset \sigma [H]$ and that $\sigma [H]\subset gHg^{-1}$, but this isn't working out.
2026-02-23 05:37:51.1771825071
All characteristic subgroups are normal
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Another way to think of normal subgroups is as subgroups which are invariant under inner automorphisms. Since characteristic subgroups are invariant under all automorphisms, they are clearly invariant under inner automorphisms, hence normal.