permCongr_eq_mul — Mathlib

English

For e ∈ Equiv.Perm α and p ∈ Perm α, the conjugation by e sends p to e p e^{-1}; i.e., e.permCongr p = e p e^{-1}.

Русский

Слабое сопряжение перестановки p сотрудниками e: e.p e^{-1}.

LaTeX

$$$$ e\,\mathrm{permCongr}\, p = e\cdot p\cdot e^{-1}. $$$$

Lean4

/-- If `e` is also a permutation, we can write `permCongr`
completely in terms of the group structure. -/
@[simp]
theorem _root_.Equiv.permCongr_eq_mul (e p : Perm α) : e.permCongr p = e * p * e⁻¹ :=
  rfl

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