Theorems · Theorem · group theory
Monoid.pow_exponent_eq_one
∀ {G : Type u} [inst : Monoid G] (g : G), g ^ Monoid.exponent G = 1- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- pow_zeroproof · cited by 1,094
- Nat.findproof · cited by 139
- Monoid.exponentstatement · cited by 128
- Nat.find_specproof · cited by 74
- Monoid.ExponentExistsproof · cited by 18
Cited by13
Results whose statement or proof uses this declaration.
- Monoid.order_dvd_exponentproof · cited by 14
- Monoid.exponent_dvd_of_monoidHomproof · cited by 5
- MonoidHom.exponent_dvdproof · cited by 5
- Monoid.exp_eq_one_iffproof · cited by 3
- Monoid.exponent_ne_zero_iff_range_orderOf_finiteproof · cited by 3
- MulAction.period_dvd_exponentproof · cited by 2
- inv_eq_self_of_exponent_twoproof · cited by 1
- Submonoid.pow_exponent_eq_oneproof · cited by 1
- mul_notMem_of_exponent_twoproof · cited by 1
- Monoid.pow_eq_mod_exponentproof · cited by 1
- Nat.Prime.exists_orderOf_eq_pow_factorization_exponentproof · cited by 1
- ArithmeticFunction.pow_carmichaelproof · cited by 0