Theorems · Theorem · group theory
Group.IsPerfect.commutator_eq_top
∀ {G : Type u_1} {inst : Group G} [self : Group.IsPerfect G], commutator G = ⊤The commutator of the group G with itself is the whole group G.
- Defined in
- Mathlib.GroupTheory.IsPerfect
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group.IsPerfect
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- commutatorstatement · cited by 56
- Group.IsPerfectstatement and proof · cited by 17
Cited by5
Results whose statement or proof uses this declaration.
- Group.IsPerfect.not_isSolvableproof · cited by 2
- Group.isPerfect_defproof · cited by 2
- SL2Simple.PSL_commutator_eq_topproof · cited by 1
- Group.IsPerfect.upperCentralSeries_eq_centerproof · cited by 1
- Group.IsPerfect.mem_commutatorproof · cited by 0