Theorems · Theorem · group theory

Representation.mem_invariants_iff_of_forall_mem_zpowers

∀ {k : Type u_1} {G : Type u_2} {V : Type u_3} [inst : CommRing k] [inst_1 : Group G] [inst_2 : AddCommGroup V]
  [inst_3 : Module k V] (ρ : Representation k G V) (g : G),
  (∀ (x : G), x ∈ Subgroup.zpowers g) → ∀ (x : V), x ∈ ρ.invariants ↔ (ρ g) x = x

Defined in

Mathlib.RepresentationTheory.Invariants

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Quot.sound

Assumes

CommRingGroupAddCommGroupModule