Hamiltonian group

GPTKB entity

Statements (20)
Predicate Object
gptkbp:instanceOf gptkb: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
gptkbp:isA gptkb: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
gptkb:William_Hamilton
gptkbp:bfsLayer 6
https://www.w3.org/2000/01/rdf-schema#label Hamiltonian group