Revision #690 → #979 · back to history
addedAbelian group2f79f04ad2d1
addedNon-abelian group53c1d5b0ff13
addedCayley table0a2d815e974b
addedAbelian iff Cayley table symmetric3143bb4fbef1
addedTrivial group is abeliand4087ba7e83d
addedIntegers under addition2ffc84d73f45
addedEvery cyclic group is abelian30a76ac06a9a
addedRing is abelian group under addition031246a4ab19
addedUnits form abelian multiplicative groupd38757e30e31
addedReal numbers as abelian groupsd2f4c5c92f89
addedSubgroups of abelian groups are normal14e76c8beaba
addedClosure under subgroups, quotients, direct sums898c40af5dfa
addedFinite simple abelian groups are cyclic of prime order843487c3bed0
addedAbelian groups equal Z-modulesc36b3e993ef2
addedMatrices and rotation matrices77b0a3caa205
addedAbelian group as Z-module92d98f1c62be
addedStructure of finitely generated abelian groups95f7f5988e53
addedSum of homomorphisms is a homomorphismb850bc2de10a
addedRank of an abelian group28b29cc50c2f
addedRank zero iff torsion668f2fdeb05a
addedCenter of a groupf6ddc3a41bb4
addedAbelian iff equal to its center554244d3332d
addedCyclic quotient by center implies abelianda6a691f9847
addedFinite abelian group as direct sum of prime-power cyclic groups69ed96c8e70e
addedGroup of prime order is cyclic5c63647ee83f
addedGroup of order p-squared is abelian14e6355b0f6d
addedFundamental theorem of finite abelian groupsa3e5155d0d88
addedCyclic group splits iff orders coprimed73b28496821
addedDecomposition of order 15 group8a3265eafb14
addedAbelian groups of order 8af7c8cb06f9c
addedAutomorphism group splits over coprime summandsad869bf70e49
addedAutomorphisms as invertible linear transformations495ca3e079bd
addedFinitely generated abelian group251371c53142
addedUnique homomorphism from free abelian group448dcce78d63
addedHomomorphism surjective with f.g. kernelf210731ef5f7
addedEquivalence with integer matricese9222b546ff3
addedSmith normal form8bfff2618cbb
addedFundamental theorem of finitely generated abelian groups6f78b9d5872c
addedInfinite cyclic group24086b40a168
addedDecomposition of finitely generated abelian groupsd8f683b6bdbc
addedDivisible group927eaa7ee160
addedClassification of divisible groupsa4619a1ff09a
addedDivisible subgroup is a direct summandcf8705a9bf03
addedInjective abelian groups are divisible (Baer)467d74655415
addedReduced abelian groupb99f0d5291a3
addedPeriodic (torsion) group0cf8bb5d4e2d
addedDirect sum of finite cyclic groups is periodic1abd29b426bf
addedPrüfer theoremsd0c327ac5170
addedUlm classification of countable p-groups04ca1c743c9c
addedTorsion-free abelian group9634b5f0a417
addedMixed abelian groupabccdc051d77
addedQuotient by torsion subgroup is torsion-freeedfc8acc205a
addedRank of an infinite abelian groupfab5832eadba
addedRank 0 groups are periodic0922184fdff9
addedFinite-rank torsion-free as subgroup of Q^n0f94e39b14ca
addedAdditive group of a ring is abelian5e5ae3dd0fef
addedCategory of abelian groups is an abelian category466c417db60a
addedFirst-order theory of abelian groups is decidable7ba3799abc3b
addedWhitehead problem undecidable in ZFC23650a02f93e
addedAdditive Group24660f716c70