Theorems · Theorem · group theory
mem_commutatorSet_of_isConj_sq
∀ (G : Type u_1) [inst : Group G] {g : G}, IsConj g (g ^ 2) → g ∈ commutatorSet GIf g is conjugate to g ^ 2, then g is a commutator
- Defined in
- Mathlib.GroupTheory.Commutator.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- pow_twoproof · cited by 150
- SemiconjByproof · cited by 99
- IsConjstatement and proof · cited by 43
- commutatorSetstatement · cited by 20
- commutatorElement_defproof · cited by 10
- IsUnit.mul_inv_cancel_rightproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsThreeCycle.mem_commutatorSet_alternatingGroupproof · cited by 1