For elements $g_i, g_j \in G$, the stabilizer of $g_j$ over this group action is the set $\{g_i \in G: g_i g_j g_i^{-1} = g_j\}$. Now, since $g_i g_j g_i^{-1} = g_j \iff g_i = g_j g_i g_j^{-1}$, would it be conclusive to describe the stabilizer as $\{g_i \in G: g_j g_i g_j^{-1} = g_i\}$?
2026-04-02 14:18:02.1775139482
Stabilizer over G acting on itself by conjugation
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