Theorems · Theorem · group theory
MonoidHom.isMulCommutative_of_isCyclic_of_ker_le_center
∀ {G : Type u_2} {G' : Type u_3} [inst : Group G] [inst_1 : Group G'] [IsCyclic G'] (f : G →* G'),
f.ker ≤ Subgroup.center G → IsMulCommutative GA group is commutative if the quotient by the center is cyclic.
Also see commGroupOfCyclicCenterQuotient for the CommGroup instance.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- one_mulproof · cited by 2,841
- mul_assocproof · cited by 1,667
- MonoidHom.rangeproof · cited by 314
- MonoidHom.kerstatement and proof · cited by 212
- Subgroup.zpowersproof · cited by 204
- zpow_negproof · cited by 198
- IsCyclicstatement and proof · cited by 122
- Subgroup.centerstatement and proof · cited by 121
Cited by1
Results whose statement or proof uses this declaration.
- isMulCommutative_of_isCyclic_quotient_center_selfproof · cited by 1