Theorems · Theorem · group theory
Subgroup.upperCentralSeries_mono
∀ (G : Type u_1) [inst : Group G], Monotone (Subgroup.upperCentralSeries G)
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 · cited by 3,593
- mul_assocproof · cited by 1,667
- Monotonestatement · cited by 1,397
- MulMemClass.mul_memproof · cited by 173
- InvMemClass.inv_memproof · cited by 52
- Subgroup.upperCentralSeriesstatement and proof · cited by 51
- monotone_nat_of_le_succproof · cited by 45
- Subgroup.Normal.conj_memproof · cited by 23
- commutatorElement_defproof · cited by 10
- Subgroup.upperCentralSeriesAuxproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Subgroup.upperCentralSeries_eq_top_iff_nilpotencyClass_leproof · cited by 5
- Subgroup.upperCentralSeries.StrictMonoOnproof · cited by 2
- Subgroup.upperCentralSeries.eq_ge_of_eq_gtproof · cited by 1
- Group.IsPerfect.upperCentralSeries_eq_centerproof · cited by 1
- upperCentralSeries_monoproof · cited by 0