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Theorems · Theorem · group theory

AddCommGroup.torsion_sum

∀ {G : Type u_1} {H : Type u_2} [inst : AddCommGroup G] [inst_1 : AddCommGroup H],
  AddCommGroup.torsion (G × H) = (AddCommGroup.torsion G).prod (AddCommGroup.torsion H)
Defined in
Mathlib.GroupTheory.Torsion
Cited by
0 results in Mathlib
Foundations
Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroupAddCommGroup
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AddCommGroup · cited by 12871AddCommGroupAddSubgroup · cited by 3232AddSubgroupIsOfFinAddOrder · cited by 105IsOfFinAddOrderAddSubgroup.prod · cited by 34AddSubgroup.prodAddCommGroup.torsion · cited by 18AddCommGroup.torsionAddSubgroup.mem_prod · cited by 4AddSubgroup.mem_prodAddCommGroup.mem_torsion · cited by 2AddCommGroup.mem_torsionIsOfFinAddOrder.prod_iff · cited by 2IsOfFinAddOrder.prod_iffAddSubgroup.ext_iff · cited by 1AddSubgroup.ext_iffAddCommGroup.torsion_sumCITED BYCITES

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