Theorems · Theorem · group theory
Subgroup.finite_quotient_of_pretransitive_of_index_ne_zero
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {X : Type u_3} [inst_1 : MulAction G X]
[MulAction.IsPretransitive G X], H.index ≠ 0 → Finite (MulAction.orbitRel.Quotient (↥H) X)- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
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- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Finitestatement · cited by 3,029
- MulActionstatement and proof · cited by 1,294
- Subgroup.indexstatement and proof · cited by 150
- MulAction.IsPretransitivestatement and proof · cited by 94
- MulAction.orbitRel.Quotientstatement and proof · cited by 28
- MulAction.pretransitive_iff_subsingleton_quotientproof · cited by 2
- Subgroup.finite_quotient_of_finite_quotient_of_index_ne_zeroproof · cited by 1
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