Theorems · Theorem · group theory
Equiv.Perm.IsCycle.orderOf
∀ {α : Type u_2} {f : Equiv.Perm α} [inst : DecidableEq α] [inst_1 : Fintype α], f.IsCycle → orderOf f = f.support.card- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Finset.cardstatement and proof · cited by 2,327
- Fintype.cardproof · cited by 1,386
- Equiv.Permstatement and proof · cited by 1,375
- orderOfstatement · cited by 324
- Equiv.Perm.supportstatement and proof · cited by 230
- Subgroup.zpowersproof · cited by 204
- Equiv.Perm.IsCyclestatement and proof · cited by 108
- Fintype.card_coeproof · cited by 72
- Fintype.card_congrproof · cited by 67
- Equiv.Perm.IsCycle.zpowersEquivSupportproof · cited by 5
- Fintype.card_zpowersproof · cited by 5
Cited by14
Results whose statement or proof uses this declaration.
- Equiv.Perm.lcm_cycleTypeproof · cited by 7
- Equiv.Perm.nodup_toListproof · cited by 5
- Equiv.Perm.IsCycle.isConjproof · cited by 2
- Equiv.Perm.next_toList_eq_applyproof · cited by 2
- Equiv.Perm.IsCycleOn.pow_apply_eqproof · cited by 2
- Equiv.Perm.pow_mod_card_support_cycleOf_self_applyproof · cited by 1
- Equiv.Perm.subgroup_eq_top_of_swap_memproof · cited by 1
- Equiv.Perm.IsCycle.pow_iffproof · cited by 1
- Equiv.Perm.closure_cycle_coprime_swapproof · cited by 1
- Equiv.Perm.closure_prime_cycle_swapproof · cited by 1
- Equiv.Perm.OnCycleFactors.kerParam_range_cardproof · cited by 1
- Equiv.Perm.cycle_zpow_mem_support_iffproof · cited by 1