Theorems · Definition · group theory
Equiv.Perm.IsCycle
{α : Type u_2} → Equiv.Perm α → PropA cycle is a non-identity permutation where any two nonfixed points of the permutation are related by repeated application of the permutation.
- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 108 results in Mathlib
- Foundations
- Depth 22 from the axioms, rests on 200 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.SameCycleproof · cited by 116
Cited by117
Results whose statement or proof uses this declaration.
- Equiv.Perm.cycleFactorsFinsetproof · cited by 96
- Equiv.Perm.mem_cycleFactorsFinset_iffstatement and proof · cited by 17
- Equiv.Perm.sum_cycleTypeproof · cited by 14
- Equiv.Perm.IsCycle.orderOfstatement and proof · cited by 14
- Equiv.Perm.IsCycle.cycleTypestatement and proof · cited by 12
- Equiv.Perm.IsCycle.ne_onestatement and proof · cited by 11
- Equiv.Perm.isCycle_cycleOfstatement · cited by 9
- Equiv.Perm.cycle_induction_onstatement and proof · cited by 8
- Equiv.Perm.toCyclestatement and proof · cited by 7
- Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iffproof · cited by 7
- Equiv.Perm.IsCycle.exists_pow_eqstatement and proof · cited by 7
- Equiv.Perm.lcm_cycleTypeproof · cited by 7