Theorems · Inductive type · group theory
Sylow
ℕ → (G : Type u_1) → [Group G] → Type u_1
A Sylow p-subgroup is a maximal p-subgroup.
- Defined in
- Mathlib.GroupTheory.Sylow
- Cited by
- 103 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 3 definitions · uses no axioms
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement · cited by 6,238
Cited by127
Results whose statement or proof uses this declaration.
- Sylow.toSubgroupstatement and proof · cited by 86
- Sylow.isPGroup'statement and proof · cited by 19
- Sylow.subtypestatement and proof · cited by 10
- MonoidHom.transferSylowstatement and proof · cited by 9
- Sylow.not_dvd_indexstatement and proof · cited by 9
- Sylow.is_maximal'statement and proof · cited by 6
- Sylow.coe_coestatement and proof · cited by 5
- Sylow.ext_iffstatement and proof · cited by 5
- alternatingGroup.two_sylow_eq_kleinFour_of_card_eq_fourstatement and proof · cited by 4
- Sylow.coe_subtypestatement and proof · cited by 4
- Sylow.mapSurjectivestatement and proof · cited by 4
- IsPGroup.toSylowstatement · cited by 3