Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
Abelian group |
| gptkbp:allElementsOrder |
2
|
| gptkbp:automorphismGroup |
gptkb:S_3
|
| gptkbp:CayleyTable |
[[e,a,b,ab],[a,e,ab,b],[b,ab,e,a],[ab,b,a,e]]
|
| gptkbp:centralTo |
gptkb:Klein_four-group
|
| gptkbp:commutative |
true
|
| gptkbp:containsElement |
a
b ab e |
| gptkbp:derivedSubgroup |
trivial group
|
| gptkbp:exponent |
2
|
| gptkbp:hasSubgroup |
gptkb:S_4
5 |
| https://www.w3.org/2000/01/rdf-schema#label |
Klein four-group
|
| gptkbp:identityElement |
e
|
| gptkbp:isomorphicTo |
gptkb:Z_2_×_Z_2
|
| gptkbp:isSimple |
false
|
| gptkbp:namedAfter |
gptkb:Felix_Klein
|
| gptkbp:notation |
gptkb:V_4
gptkb:Z_2_×_Z_2 |
| gptkbp:order |
4
|
| gptkbp:presentedBy |
a^2 = b^2 = (ab)^2 = e
|
| gptkbp:usedIn |
gptkb:geometry
gptkb:Galois_theory abstract algebra group theory |
| gptkbp:bfsParent |
gptkb:Felix_Klein
gptkb:group_of_people |
| gptkbp:bfsLayer |
4
|