toPermHom_apply_toCentralizer — Mathlib

English

The application of toPermHom g to the centralizer image equals the original τ: (toPermHom g)(toCentralizer a τ) = τ.

Русский

Применение toPermHom g к образу центральизатора равно исходному τ: (toPermHom g)(toCentralizer a τ) = τ.

LaTeX

$$$(toPermHom\\ g)(toCentralizer\\;a\\;\\tau) = (\\tau : Perm\\ g.cycleFactorsFinset)$$$

Lean4

theorem toPermHom_apply_toCentralizer : (toPermHom g) (toCentralizer a τ) = (τ : Perm g.cycleFactorsFinset) :=
  by
  apply ext
  intro c
  rw [OnCycleFactors.toPermHom_apply, toCentralizer_equivariant]

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