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\begintheorem[Orbit–Stabilizer] Let $G$ act on $A$ and $a\in A$. Then $|\mathcalO_a| = [G : G_a]$, where $\mathcalO_a = \g\cdot a \mid g\in G\$. \endtheorem Another aspect: the user might be a student
\beginproof The group $G$ acts on itself by conjugation. The orbit of an element $x$ under this action is its conjugacy class, denoted $\mathcalO_x$ or $\textCl(x)$. The stabilizer of $x$ is the centralizer $C_G(x) = \g \in G \mid gxg^-1 = x\$. The orbit of an element $x$ under this
By 4:30 AM, the "full" solution set was complete. The document was a masterpiece of commutative diagrams and perfectly aligned equalities.
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