Theorems · Theorem · group theory
Subgroup.card_commutator_dvd_index_center_pow
∀ (G : Type u_1) [inst : Group G] [Finite ↑(commutatorSet G)], Nat.card ↥(commutator G) ∣ (Subgroup.center G).index ^ ((Subgroup.center G).index * Nat.card ↑(commutatorSet G) + 1)
If G has n commutators [g₁, g₂], then |G'| ∣ [G : Z(G)] ^ ([G : Z(G)] * n + 1),
where G' denotes the commutator of G.
- Defined in
- Mathlib.GroupTheory.Schreier
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Elemstatement and proof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- LE.le.transproof · cited by 3,151
- Finitestatement and proof · cited by 3,029
- zero_addproof · cited by 2,366
- MulZeroClass.zero_mulproof · cited by 1,625
- pow_oneproof · cited by 894
- Nat.cardstatement and proof · cited by 844
- pow_succproof · cited by 374
- MonoidHom.kerproof · cited by 212
- Subgroup.indexstatement and proof · cited by 150
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.card_commutator_le_of_finite_commutatorSetproof · cited by 0