Theorems · Theorem · group theory
IsZGroup.isCyclic_commutator
∀ (G : Type u_1) [inst : Group G] [Finite G] [IsZGroup G], IsCyclic ↥(commutator G)
A finite Z-group has cyclic commutator subgroup.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites47
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Bot.botproof · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- Finitestatement and proof · cited by 3,029
- MulEquivproof · cited by 1,142
- eq_or_neproof · cited by 1,117
- CommGroupproof · cited by 990
- Bracket.bracketproof · cited by 642
- MulEquiv.symmproof · cited by 482
- le_topproof · cited by 411
Cited by1
Results whose statement or proof uses this declaration.
- isZGroup_iff_exists_mulEquivproof · cited by 0