Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:associative |
yes
|
| gptkbp:example |
nonzero complex numbers under multiplication
nonzero rational numbers under multiplication nonzero real numbers under multiplication nonzero elements of a finite field |
| gptkbp:field |
group of nonzero elements under multiplication
|
| gptkbp:hasInverseElement |
yes
|
| https://www.w3.org/2000/01/rdf-schema#label |
Multiplicative group
|
| gptkbp:identityElement |
1
|
| gptkbp:isNonAbelian |
yes
|
| gptkbp:notation |
G×
|
| gptkbp:operator |
multiplication
|
| gptkbp:order |
order of the group depends on the underlying set
|
| gptkbp:property |
associativity
closure under multiplication existence of identity element existence of inverses |
| gptkbp:relatedTo |
additive group
|
| gptkbp:usedIn |
abstract algebra
number theory |
| gptkbp:bfsParent |
gptkb:Algebraic_groups
|
| gptkbp:bfsLayer |
7
|