Theorems · Theorem · group theory
AddSubgroup.subgroupOf_inertia
∀ {M : Type u_6} [inst : AddGroup M] (I : AddSubgroup M) {G : Type u_7} [inst_1 : Group G] [inst_2 : MulAction G M]
(H : Subgroup G), (I.inertia G).subgroupOf H = I.inertia ↥H- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- AddGroupstatement and proof · cited by 4,410
- Subgroupstatement and proof · cited by 3,593
- AddSubgroupstatement and proof · cited by 3,232
- MulActionstatement and proof · cited by 1,294
- Subgroup.subgroupOfstatement · cited by 122
- AddSubgroup.inertiastatement · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.card_stabilizer_eq_card_inertia_mul_finrankproof · cited by 2
- AddSubgroup.inertia_map_subtypeproof · cited by 1