Mathlib Map

Theorems · Definition · group theory

IsCyclic.commGroup

{α : Type u_1} → [inst : Group α] → [IsCyclic α] → CommGroup α

A cyclic group is always commutative. This is not an instance because often we have a better proof of CommGroup.

Defined in
Mathlib.GroupTheory.SpecificGroups.Cyclic.Basic
Cited by
2 results in Mathlib
Foundations
Depth 35 from the axioms · uses propext
Assumes
GroupIsCyclic

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites3

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
  • CommGroupstatement · cited by 990
  • IsCyclicstatement and proof · cited by 122

Cited by2

Results whose statement or proof uses this declaration.