Theorems · Theorem · group theory
not_isCyclic_prod_of_infinite_nontrivial
∀ (M : Type u_4) (N : Type u_5) [inst : Group M] [inst_1 : Group N] [Infinite M] [Nontrivial N], ¬IsCyclic (M × N)
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupGroupInfiniteNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Nontrivialstatement and proof · cited by 2,416
- Additiveproof · cited by 356
- Infinitestatement and proof · cited by 352
- IsCyclicstatement · cited by 122
- AddEquiv.prodAdditiveproof · cited by 4
- AddEquiv.isAddCyclicproof · cited by 4
- isAddCyclic_additive_iffproof · cited by 3
- not_isAddCyclic_prod_of_infinite_nontrivialproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Group.isCyclic_prod_iffproof · cited by 2