Theorems · Theorem · group theory

IsMulIndecomposable.pairwise_div_notMem_range

∀ {ι : Type u_1} {G : Type u_3} [inst : CommGroup G] [inst_1 : InvolutiveInv ι] (v : ι → G),
  (∀ (i : ι), v i ≠ 1) →
    (∀ (i : ι), v i⁻¹ = (v i)⁻¹) →
      ∀ (s t : Set ι),
        s ⊆ {i | IsMulIndecomposable v t i} →
          (∀ (i : ι), i ∈ t ∨ i⁻¹ ∈ t) → s.Pairwise fun i j => v i / v j ∉ Set.range v

Defined in

Mathlib.Algebra.Group.Irreducible.Indecomposable

Cited by

1 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupInvolutiveInv