Theorems · Definition · group theory
Monoid.ExponentExists
(G : Type u) → [Monoid G] → Prop
A predicate on a monoid saying that there is a positive integer n such that g ^ n = 1
for all g.
- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
Cited by19
Results whose statement or proof uses this declaration.
- Monoid.exponentproof · cited by 128
- Monoid.pow_exponent_eq_oneproof · cited by 13
- Monoid.exponent_eq_zero_iffstatement · cited by 5
- Monoid.exponent_eq_zero_of_order_zeroproof · cited by 4
- Monoid.exponent_ne_zerostatement and proof · cited by 4
- ExponentExists.isMulTorsionstatement and proof · cited by 2
- Monoid.exponent_eq_iSup_orderOfproof · cited by 2
- Monoid.ExponentExists.exponent_ne_zerostatement · cited by 2
- Monoid.ExponentExists.exponent_posstatement · cited by 2
- Monoid.ExponentExists.of_finitestatement · cited by 2
- Monoid.ExponentExists.orderOf_posstatement and proof · cited by 2
- Monoid.orderOf_le_exponentstatement and proof · cited by 1