AbelianGroup

Available

Represents an abelian group specified by invariant factors

Forms

AbelianGroup[{n1, n2, …}]

Verified examplesAbelianGroup[{2, 2, 3}]//GroupOrder → 12 AbelianGroup[{2, 2, 3}]//GroupElements → {Cycles[{}], Cycles[{{5, 6, 7}}], Cycles[{{5, 7, 6}}], Cycles[{{3, 4}}], Cycles[{{3, 4}, {5, 6, 7}}], Cycles[{{3, 4}, {5, 7, 6}}], Cycles[{{1, 2}}], Cycles[{{1, 2}, {5, 6, 7}}], Cycles[{{1, 2}, {5, 7, 6}}], Cycles[{{1, 2}, {3, 4}}], Cycles[{{1, 2}, {3, 4}, {5, 6, 7}}], Cycles[{{1, 2}, {3, 4}, {5, 7, 6}}]}AbelianGroup[{2, 2, 3}]//GroupGenerators → {Cycles[{{1, 2}}], Cycles[{{3, 4}}], Cycles[{{5, 6, 7}}]}

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Topics

Group Theory - Named Groups »
Named Groups - Parametrized Infinite Families
New In80 Alphabetical Listing - A

Related

SymmetricGroup CyclicGroup PermutationGroup Cycles AlternatingGroup DihedralGroup AcyclicGraphQ AdjacencyGraph AdjacencyMatrix Annuity AnnuityDue ArcSinDistribution

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