Statements (59)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:alsoKnownAs |
abelian group
|
| gptkbp:example |
real numbers under addition
integers under addition nonzero real numbers under multiplication vector space under addition |
| gptkbp:generalizes |
gptkb:illustrator
gptkb:operating_system gptkb:Pontryagin_duality automorphism homomorphism trivial group subfamily endomorphism group cohomology isomorphism cyclic group quotient group group action group extension group representation torsion group finite abelian 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:algebraic_geometry
gptkb:topology Fourier analysis chemistry coding theory cryptography number theory physics representation theory combinatorics 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
|
| https://www.w3.org/2000/01/rdf-schema#label |
commutative group
|
| gptkbp:namedAfter |
gptkb:Niels_Henrik_Abel
|
| gptkbp:studiedIn |
group theory
|
| gptkbp:bfsParent |
gptkb:torus_group
|
| gptkbp:bfsLayer |
5
|