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A division (or rational conjugacy classes) of a finite group $G$ is an equivalence class under the following relation: $x \sim y$ if there exist $g \in G$ and $n \in \Z$ relatively prime to the order of $x$ with $y = g^{-1} x^n g$. It is a coarsening of conjugacy: any division is a union of conjugacy classes.

Just as values of characters are constant on conjugacy classes, values of rational characters are constant on rational conjugacy classes.

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  • Review status: reviewed
  • Last edited by John Jones on 2022-07-02 18:49:45
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