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Theorems · Theorem · group theory

IsZGroup.isZGroup

∀ {G : Type u_1} {inst : Group G} [self : IsZGroup G] (p : ℕ), Nat.Prime p → ∀ (P : Sylow p G), IsCyclic ↥↑P
Defined in
Mathlib.GroupTheory.SpecificGroups.ZGroup
Cited by
1 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext
Assumes
IsZGroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsZGroup.commutator_lt · cited by 0IsZGroup.commutator_ltGroup · cited by 6238GroupSubgroup · cited by 3593SubgroupNat.Prime · cited by 2059Nat.PrimeIsCyclic · cited by 122IsCyclicSylow · cited by 103SylowSylow.toSubgroup · cited by 86Sylow.toSubgroupIsZGroup · cited by 12IsZGroupIsZGroup.isZGroupCITED BYCITES

Cites7

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Cited by1

Results whose statement or proof uses this declaration.