Theorems · Theorem · commutative algebra
Int.subgroup_index_ne_zero_iff
∀ {ι : Type u_1} [Finite ι] {H : Subgroup (ι → Multiplicative ℤ)}, H.index ≠ 0 ↔ Nonempty (↥H ≃* (ι → Multiplicative ℤ))- Defined in
- Mathlib.LinearAlgebra.FreeModule.Int
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
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Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Subgroupstatement and proof · cited by 3,593
- Finitestatement and proof · cited by 3,029
- MulEquivstatement and proof · cited by 1,142
- AddEquivproof · cited by 1,087
- Multiplicativestatement and proof · cited by 875
- MulEquiv.symmproof · cited by 482
- MonoidHomClass.toMonoidHomproof · cited by 294
- Subgroup.comapproof · cited by 154
- Subgroup.indexstatement and proof · cited by 150
- MulEquiv.transproof · cited by 53
- AddEquiv.transproof · cited by 53
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