Theorems · Theorem · group theory
pow_orderOf_eq_one
∀ {G : Type u_1} [inst : Monoid G] (x : G), x ^ orderOf x = 1- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 21 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
- Nat.iterateproof · cited by 740
- orderOfstatement and proof · cited by 324
- Function.minimalPeriodproof · cited by 100
- Function.isPeriodicPt_minimalPeriodproof · cited by 11
- mul_left_iterate_apply_oneproof · cited by 3
Cited by30
Results whose statement or proof uses this declaration.
- pow_mod_orderOfproof · cited by 12
- IsPrimitiveRoot.orderOfproof · cited by 10
- zpow_mod_orderOfproof · cited by 6
- Equiv.Perm.IsThreeCycle.support_eq_iff_mem_supportproof · cited by 3
- Equiv.Perm.IsCycle.pow_eq_one_iffproof · cited by 3
- orderOf_map_dvdproof · cited by 3
- QuaternionGroup.orderOf_a_oneproof · cited by 2
- minpoly_algEquiv_toLinearMapproof · cited by 2
- exists_orderOf_eq_prime_pow_iffproof · cited by 2
- zpow_pow_orderOfproof · cited by 2
- MulAction.period_dvd_orderOfproof · cited by 2
- DihedralGroup.orderOf_r_oneproof · cited by 2