Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
cyclic group
|
| gptkbp:automorphismGroup |
gptkb:Z_2_×_Z_2
|
| gptkbp:containsElement |
2
0 1 10 11 3 4 5 6 7 8 9 |
| gptkbp:generation |
1
11 5 7 |
| gptkbp:hasElementOrder |
2
1 12 3 4 6 |
| gptkbp:hasSubgroup |
gptkb:Z_2
gptkb:Z_3 gptkb:Z_6 gptkb:Z_4 Z_24 |
| https://www.w3.org/2000/01/rdf-schema#label |
Z 12
|
| gptkbp:identityElement |
0
|
| gptkbp:isDirectProductOfCyclicGroups |
true
|
| gptkbp:isFinite |
true
|
| gptkbp:isHomomorphicImageOf |
Z
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isomorphicTo |
C_12
Z_3 × Z_4 |
| gptkbp:isQuotientOf |
Z
|
| gptkbp:isSimple |
false
|
| gptkbp:isTorsionGroup |
true
|
| gptkbp:notation |
Z/12Z
C_12 ℤ/12ℤ |
| gptkbp:operator |
addition modulo 12
|
| gptkbp:order |
12
|
| gptkbp:quotientMap |
n ↦ n mod 12
|
| gptkbp:usedIn |
group theory
modular arithmetic |
| gptkbp:bfsParent |
gptkb:Z_6_×_Z_2
|
| gptkbp:bfsLayer |
8
|