Theorems · Inductive type · group theory
IsCyclic
(G : Type u) → [Pow G ℤ] → Prop
A group is called cyclic if it is generated by a single element. [Wikidata Q245462](https://www.wikidata.org/wiki/Q245462)
- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 122 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 3 definitions · uses no axioms
- Assumes
- Pow
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by140
Results whose statement or proof uses this declaration.
- IsCyclic.exists_generatorstatement and proof · cited by 14
- isCyclic_of_surjectivestatement and proof · cited by 14
- LinearOrderedCommGroup.Subgroup.genLTOnestatement and proof · cited by 12
- IsCyclic.exponent_eq_cardstatement and proof · cited by 7
- IsCyclic.iff_exponent_eq_cardstatement and proof · cited by 6
- IsCyclic.mulAutMulEquivstatement and proof · cited by 6
- LinearOrderedCommGroup.Subgroup.genLTOne_uniquestatement and proof · cited by 5
- MulEquiv.isCyclicstatement and proof · cited by 5
- zmodCyclicMulEquivstatement and proof · cited by 5
- Subgroup.isCyclic_iff_exists_zpowers_eq_topstatement · cited by 4
- isCyclic_iff_exists_zpowers_eq_topstatement and proof · cited by 4
- isCyclic_of_card_dvd_primestatement · cited by 4