Theorems · Theorem · group theory

Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_norm

∀ (k : Type u) {G : Type u} [inst : CommRing k] [inst_1 : CommGroup G] [inst_2 : Fintype G] (g : G),
  (∀ (x : G), x ∈ Subgroup.zpowers g) →
    (Rep.Hom.hom ((Rep.leftRegular k G).applyAsHom g - CategoryTheory.CategoryStruct.id (Rep.leftRegular k G))).range =
      (Rep.Hom.hom (Rep.leftRegular k G).norm).ker

Defined in

Mathlib.RepresentationTheory.Homological.FiniteCyclic

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommGroupFintype