Theorems · Theorem · group theory
Subgroup.Normal.mem_comm_iff
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G}, H.Normal → ∀ {a b : G}, a * b ∈ H ↔ b * a ∈ H- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Subgroupstatement and proof · cited by 3,593
- Subgroup.Normalstatement and proof · cited by 334
- Subgroup.Normal.mem_commproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Subgroup.normalizer_eq_top_iffproof · cited by 10
- Equiv.Perm.not_isSolvable_fin_5proof · cited by 2
- QuotientGroup.eq_iff_div_memproof · cited by 2
- eq_cosets_of_normalproof · cited by 1