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Diff — Klein four-group

Revision #1337 → #2113 · back to history

modifiedIsomorphic to dihedral group of order 471f458b93850
FieldFrom #1337To #2113
mathlib.declDihedralGroup.instIsKleinFourDihedralGroup.instIsKleinFourOfNatNat
noteThe instance `IsKleinFour (DihedralGroup 2)` combined with `IsKleinFour.nonempty_mulEquiv` gives the isomorphism with any Klein four-group.The anonymous instance `IsKleinFour (DihedralGroup 2)` (auto-named `DihedralGroup.instIsKleinFourOfNatNat`) combined with `IsKleinFour.nonempty_mulEquiv` gives the isomorphism with any Klein four-group.
addedOnly abelian dihedral group besides order 205c2a8c8d32d
modifiedIsomorphic to direct sum Z2⊕Z26ddb57cc76ae
FieldFrom #1337To #2113
mathlib.declIsAddKleinFour.instZModProdinstIsAddKleinFourProdZModOfNatNat
noteThe instance `IsAddKleinFour (ZMod 2 × ZMod 2)` together with `IsAddKleinFour.nonempty_addEquiv` provides the isomorphism.The anonymous instance `IsAddKleinFour (ZMod 2 × ZMod 2)` (auto-named `instIsAddKleinFourProdZModOfNatNat`) together with `IsAddKleinFour.nonempty_addEquiv` provides the isomorphism.
addedTransitive subgroup of S_4 as a Galois groupd1752198d087
addedKernel of S_4 → S_3911a55de6e56
addedQuotient of units of split-complex numbersed041f73d61d