Theorems · Theorem · group theory
isMulCommutative_of_isCyclic_quotient_center_self
∀ (G : Type u_2) [inst : Group G] [IsCyclic (G ⧸ Subgroup.center G)], IsMulCommutative G
If the quotient by the center of a group is cyclic, then the group is commutative.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- HasQuotient.Quotientstatement and proof · cited by 2,301
- MonoidHom.kerproof · cited by 212
- IsCyclicstatement and proof · cited by 122
- Subgroup.centerstatement and proof · cited by 121
- IsMulCommutativestatement · cited by 95
- QuotientGroup.mk'proof · cited by 90
- QuotientGroup.ker_mk'proof · cited by 18
- MonoidHom.isMulCommutative_of_isCyclic_of_ker_le_centerproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsPGroup.isMulCommutative_of_card_eq_prime_sqproof · cited by 0