class equation

《近世代数》 · 第 75 页

我们把 (25) 式称为有限群 $G$ 的类方程。

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《Algebra》 · 第 89–90 页 · Chapter II，Section 4「The Action of a Group on a Set」，Corollary 4.4 及其后定名段

Corollary 4.4. Let $G$ be a finite group and $K$ a subgroup of $G$. (i) The number of elements in the conjugacy class of $x\in G$ is $[G:C_G(x)]$, which divides $|G|$; (ii) if $\bar{x}_1,\ldots,\bar{x}_n$ $(x_i\in G)$ are the distinct conjugacy classes of $G$, then $|G|=\sum_{i=1}^{n}[G:C_G(x_i)]$; (iii) the number of subgroups of $G$ conjugate to $K$ is $[G:N_G(K)]$, which divides $|G|$. […] The equation $|G|=\sum_{i=1}^{n}[G:C_G(x_i)]$ as in Corollary 4.4(ii) is called the class equation of the finite group $G$.