Theorems · Theorem · group theory
Subgroup.le_normalizer
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G}, H ≤ Subgroup.normalizer ↑H- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- SetLike.mem_coeproof · cited by 302
- Subgroup.normalizerstatement · cited by 108
- Subgroup.inv_memproof · cited by 40
- Subgroup.mul_mem_cancel_rightproof · cited by 7
- Subgroup.mul_mem_cancel_leftproof · cited by 5
Cited by19
Results whose statement or proof uses this declaration.
- IsPGroup.to_sup_of_normal_right'proof · cited by 2
- IsCyclic.normalizer_le_centralizerproof · cited by 2
- IsPGroup.inf_normalizer_sylowproof · cited by 1
- Sylow.card_normalizer_modEq_cardproof · cited by 1
- Sylow.normal_of_all_max_subgroups_normalproof · cited by 1
- Sylow.normal_of_normalizer_normalproof · cited by 1
- Sylow.normalizer_le_centralizer_or_le_commutatorproof · cited by 1
- Sylow.normalizer_normalizerproof · cited by 1
- Sylow.not_dvd_index'proof · cited by 1
- Subgroup.normal_subgroupOf_of_le_normalizerproof · cited by 1
- MonoidHom.transferSylow_eq_pow_auxproof · cited by 1
- Subgroup.self_le_normalizer_lowerCentralSeriesproof · cited by 1