|
gptkbp:instance_of
|
gptkb:musical_group
|
|
gptkbp:character_traits
|
Klein four-group V4
|
|
gptkbp:element
|
gptkb:r
s
e
r^2
sr
r^3
sr^2
sr^3
|
|
gptkbp:has_applications_in
|
gptkb:Graphics_Processing_Unit
pattern recognition
molecular symmetry
|
|
gptkbp:has_exhibition
|
<r,s | r^4 = e, s^2 = e, srs = r^3>
|
|
gptkbp:has_order_of_elements
|
1 for e
2 for s
2 for sr
2 for sr^2
2 for sr^3
4 for r
|
|
gptkbp:has_produced
|
r,s
|
|
gptkbp:has_subgroup
|
gptkb:S4
V4
Z(D4)
|
|
gptkbp:has_symmetries
|
4 reflections
4 rotations
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
D4
|
|
gptkbp:is_a_center_for
|
Z(D4) = {e, r^2}
|
|
gptkbp:is_finite_group
|
gptkb:true
|
|
gptkbp:is_non_abelian
|
gptkb:true
|
|
gptkbp:is_related_to
|
gptkb:Mathematics
geometry
symmetry
|
|
gptkbp:is_represented_in
|
2x2 matrices
quaternions
|
|
gptkbp:is_studied_in
|
gptkb:topology
abstract algebra
combinatorics
discrete mathematics
group representation theory
|
|
gptkbp:is_symmetry_group
|
gptkb:Square
|
|
gptkbp:is_used_in
|
gptkb:crypt
gptkb:computer_science
gptkb:robotics
gptkb:musical_group
chemistry
physics
|
|
gptkbp:order
|
8
|
|
gptkbp:bfsParent
|
gptkb:Audi_A8
gptkb:S4
gptkb:World_Chess_Championship_1974
gptkb:The_S._8_Series
gptkb:Fischer-Korchnoi_1970
|
|
gptkbp:bfsLayer
|
5
|