Theorems · Theorem · group theory
IsTorsion.extension_closed
Deprecated since 2026-06-30Use IsMulTorsion.extension_closed instead.
∀ {G : Type u_1} {H : Type u_2} [inst : Group G] {N : Subgroup G} [inst_1 : Group H] {f : G →* H},
N = f.ker → IsMulTorsion H → IsMulTorsion ↥N → IsMulTorsion GAlias of IsMulTorsion.extension_closed.
Torsion groups are closed under extensions.
- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement · cited by 6,238
- MonoidHomstatement · cited by 3,629
- Subgroupstatement · cited by 3,593
- MonoidHom.kerstatement · cited by 212
- IsMulTorsionstatement · cited by 35
- IsMulTorsion.extension_closedproof · cited by 2
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