Statements (57)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:alsoKnownAs |
gptkb:abelian_group
|
| gptkbp:example |
real numbers under addition
integers under addition nonzero real numbers under multiplication vector space under addition |
| gptkbp:generalizes |
gptkb:subfamily
gptkb:finite_abelian_group gptkb:illustrator gptkb:operating_system gptkb:isomorphism gptkb:Pontryagin_duality gptkb:cyclic_group gptkb:automorphism gptkb:quotient_group homomorphism trivial group endomorphism group cohomology group action group extension group representation torsion group free abelian group torsion subgroup direct product of groups order of element order of group fundamental theorem of finitely generated abelian groups direct sum of groups divisible group rank of abelian group torsion-free abelian group |
| gptkbp:hasApplication |
gptkb:combinatorics
gptkb:algebraic_geometry gptkb:topology Fourier analysis chemistry coding theory cryptography number theory physics representation theory homological algebra module theory |
| gptkbp:hasAxiom |
for all a, b in G, a * b = b * a
for all a, b, c in G, (a * b) * c = a * (b * c) there exists e in G such that for all a in G, e * a = a * e = a for all a in G, there exists b in G such that a * b = b * a = e |
| gptkbp:hasProperty |
associativity
commutativity identity element inverse element |
| gptkbp:hasSubgroup |
gptkb:group_of_people
|
| gptkbp:namedAfter |
gptkb:Niels_Henrik_Abel
|
| gptkbp:studiedIn |
group theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
commutative group
|