commutatorElement_eq_one_iff_mul_comm

English

If H is commensurable with K, then for any g, commensurator H equals commensurator (g • H) and (g • K).

Русский

Если H коммensурируемо относительно K, то для любого g равны commensurator(H) и commensurator(g • H) и commensurator(g • K).

LaTeX

$$H.Commensurable K → commensurator H = commensurator (instHSMul.hSMul g H)$$

Lean4

theorem commutatorElement_eq_one_iff_mul_comm : ⁅g₁, g₂⁆ = 1 ↔ g₁ * g₂ = g₂ * g₁ := by
  rw [commutatorElement_def, mul_inv_eq_one, mul_inv_eq_iff_eq_mul]

Похожие утверждения