Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
group theory concept
|
| gptkbp:class |
finite Hamiltonian groups are isomorphic to the direct product of the quaternion group Q8, an elementary abelian 2-group, and an abelian group of odd order
|
| gptkbp:defines |
A non-abelian group in which every subgroup is normal
|
| gptkbp:example |
gptkb:quaternion_group_Q8
direct product of Q8 and an abelian group of odd order and an elementary abelian 2-group |
| https://www.w3.org/2000/01/rdf-schema#label |
Hamiltonian group
|
| gptkbp:isA |
non-abelian group
|
| gptkbp:namedAfter |
gptkb:William_Rowan_Hamilton
|
| gptkbp:property |
non-abelian
all elements have order 2 or 4 or odd order center is nontrivial every finite Hamiltonian group is a Dedekind group every subgroup is normal infinite Hamiltonian groups exist |
| gptkbp:relatedTo |
gptkb:Dedekind_group
gptkb:quaternion_group |
| gptkbp:studiedIn |
group theory
|
| gptkbp:bfsParent |
gptkb:William_Rowan_Hamilton
|
| gptkbp:bfsLayer |
4
|