class equation theoremClassEquationTheorem2004-05-01 16:17:542004-05-24 17:13:12Theorem% this is the default PlanetMath preamble. as your knowledge
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% define commands hereLet $G$ be a group acting on a finite set $X$. Define the set of invariants in $X$ by the action of $G$ as $G_{X}=\{x \in X \quad \lvert \quad gx=x \quad \forall g \in G\}$. Then there are $H_{1}, ..., H_{r}$ subgroups of $G$ with $H_{i} \neq G \quad \forall i$ such that
$\#X = \#G_{X} + \sum_{i=1}^{r}[G:H_{i}]$