Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:category |
gptkb:algebra
|
| gptkbp:closed |
closed under multiplication
|
| gptkbp:consistsOf |
complex roots of unity
|
| gptkbp:containsElement |
e^{2πik/n} (for k=0,...,n-1)
|
| gptkbp:everyElementSatisfies |
z^n = 1
|
| gptkbp:generation |
primitive n-th root of unity
|
| gptkbp:hasSubgroup |
multiplicative group of nonzero complex numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
Roots of unity group
|
| gptkbp:identityElement |
1
complex conjugate |
| gptkbp:isA |
finite cyclic group
subgroup of multiplicative group of complex numbers |
| gptkbp:isNonAbelian |
true
|
| gptkbp:isomorphicTo |
cyclic group of order n
|
| gptkbp:notation |
μ_n
|
| gptkbp:operator |
multiplication
|
| gptkbp:order |
n (for n-th roots of unity)
|
| gptkbp:relatedTo |
gptkb:cyclotomic_polynomial
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:Galois_theory gptkb:discrete_Fourier_transform Fourier analysis number theory representation theory cyclotomic fields |
| gptkbp:bfsParent |
gptkb:Cyclotomic_fields
|
| gptkbp:bfsLayer |
8
|