Theorems · Theorem · group theory
orderOf_one
∀ {G : Type u_1} [inst : Monoid G], orderOf 1 = 1- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 22 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.
Cites5
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
- orderOfstatement · cited by 324
- Function.minimalPeriodproof · cited by 100
- Function.minimalPeriod_idproof · cited by 2
- one_mul_eq_idproof · cited by 1
Cited by15
Results whose statement or proof uses this declaration.
- Equiv.Perm.lcm_cycleTypeproof · cited by 7
- orderOf_neg_oneproof · cited by 5
- ZMod.orderOf_one_add_mul_prime_powproof · cited by 2
- mul_notMem_of_orderOf_eq_twoproof · cited by 1
- Nat.Prime.exists_orderOf_eq_pow_factorization_exponentproof · cited by 1
- Monoid.exponent_eq_prime_iffproof · cited by 1
- MonoidHom.FixedPointFree.orderOf_ne_two_of_involutiveproof · cited by 1
- Monoid.exists_orderOf_eq_exponentproof · cited by 1
- FiniteField.card_cast_subgroup_card_ne_zeroproof · cited by 0
- LinearOrderedRing.orderOf_le_twoproof · cited by 0
- Equiv.Perm.orderOf_cycleOf_dvd_orderOfproof · cited by 0
- gaussSum_pow_eq_prod_jacobiSumproof · cited by 0