center — Mathlib

English

Reiterating the NPow characterization of saturated subgroups.

Русский

Повторно характеризуем насыщенность подгрупп через NPow.

LaTeX

$$Saturated(H) ↔ ∀ (n : Nat) (g : G), g ^ n ∈ H → n = 0 ∨ g ∈ H$$

Lean4

/-- The center of a multiplication with unit `M` is the set of elements that commute with everything
in `M` -/
@[to_additive /-- The center of an addition with zero `M` is the set of elements that commute with everything in
    `M` -/
    ]
def center : Submonoid M where
  carrier := Set.center M
  one_mem' := Set.one_mem_center
  mul_mem' := Set.mul_mem_center

Похожие утверждения