mulEquivOfOrderOfEq_symm_apply_gen

English

The index of the range of powMonoidHom d equals |G| / gcd(|G|, d) for a cyclic finite G.

Русский

Индекс образа powMonoidHom d равен |G| / gcd(|G|, d) для циклической конечной G.

LaTeX

$$(powMonoidHom d).range.index = |G| gcd d$$

Lean4

@[to_additive] -- `simp` can prove this by a combination of the two preceding lemmas

theorem mulEquivOfOrderOfEq_symm_apply_gen : (mulEquivOfOrderOfEq hg hg' h).symm g' = g :=
  monoidHomOfForallMemZpowers_apply_gen hg' h.dvd

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