Theorems · Theorem · number theory
MulChar.mem_subgroupOrderIsoSubgroupMulChar_symm_iff
∀ {M : Type u_1} {R : Type u_2} [inst : CommMonoid M] [inst_1 : CommRing R] [inst_2 : Finite M]
[inst_3 : HasEnoughRootsOfUnity R (Monoid.exponent Mˣ)] {X : Subgroup (MulChar M R)} {m : Mˣ},
m ∈ (MulChar.subgroupOrderIsoSubgroupMulChar M R).symm (OrderDual.toDual X) ↔ ∀ χ ∈ X, χ ↑m = 1- Defined in
- Mathlib.NumberTheory.MulChar.Duality
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Equivstatement · cited by 8,337
- MonoidHomproof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Finitestatement and proof · cited by 3,029
- Unitsstatement and proof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- Units.valstatement and proof · cited by 1,966
- OrderDualstatement · cited by 927
- OrderIsostatement · cited by 874
- OrderDual.toDualstatement and proof · cited by 481
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