Theorems · Theorem · group theory

CommGroup.mem_subgroupOrderIsoSubgroupMonoidHom_symm_iff

∀ {G : Type u_1} (M : Type u_2) [inst : CommGroup G] [inst_1 : Finite G] [inst_2 : CommMonoid M]
  [hM : HasEnoughRootsOfUnity M (Monoid.exponent G)] (Φ : Subgroup (G →* Mˣ)) (g : G),
  g ∈ (CommGroup.subgroupOrderIsoSubgroupMonoidHom G M).symm (OrderDual.toDual Φ) ↔ ∀ φ ∈ Φ, φ g = 1

Defined in

Mathlib.GroupTheory.FiniteAbelian.Duality

Cited by

0 results in Mathlib

Foundations

Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupFiniteCommMonoidHasEnoughRootsOfUnity