Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:alsoKnownAs |
gptkb:Q8
|
| gptkbp:centralTo |
{1, -1}
|
| gptkbp:containsElement |
{1, -1, i, -i, j, -j, k, -k}
|
| gptkbp:generation |
i
j |
| gptkbp:hasElementOrder |
2
1 4 |
| gptkbp:hasExponent |
4
|
| gptkbp:hasSubgroup |
gptkb:Klein_four-group
gptkb:quaternion_group cyclic group of order 4 |
| https://www.w3.org/2000/01/rdf-schema#label |
quaternion group of order 8
|
| gptkbp:isHamiltonian |
true
|
| gptkbp:isNilpotent |
true
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isNonCyclic |
true
|
| gptkbp:isomorphicTo |
group of unit quaternions {±1, ±i, ±j, ±k}
|
| gptkbp:isSimple |
false
|
| gptkbp:isSmallestNonAbelianHamiltonianGroup |
true
|
| gptkbp:isSolvable |
true
|
| gptkbp:order |
8
|
| gptkbp:presentedBy |
<i, j | i^4 = 1, i^2 = j^2, ij = ji^{-1}>
|
| gptkbp:usedIn |
abstract algebra
group theory representation theory |
| gptkbp:bfsParent |
gptkb:Dedekind_group
|
| gptkbp:bfsLayer |
6
|