Theorems · Theorem · group theory
IsCyclic.ext
∀ {G : Type u_2} [inst : Group G] [Finite G] [IsCyclic G] {d : ℕ} {a b : ZMod d},
Nat.card G = d → (∀ (t : G), t ^ a.val = t ^ b.val) → a = b- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Finitestatement and proof · cited by 3,029
- ZModstatement and proof · cited by 1,024
- Nat.cardstatement and proof · cited by 844
- Nat.ModEqproof · cited by 225
- Subgroup.zpowersproof · cited by 204
- ZMod.valstatement and proof · cited by 159
- IsCyclicstatement and proof · cited by 122
- ZMod.natCast_valproof · cited by 27
- IsCyclic.exists_generatorproof · cited by 14
- orderOf_eq_card_of_forall_mem_zpowersproof · cited by 13
- ZMod.natCast_eq_natCast_iffproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- modularCyclotomicCharacter.toFun_uniqueproof · cited by 3