Statements (393)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
gptkb:group_of_people gptkb:mathematical_concept gptkb:organization fictional organization Teilgebiet der Mathematik |
| gptkbp:A_1_is_trivial_group |
true
|
| gptkbp:A_2_is_trivial_group |
true
|
| gptkbp:A_3_is_abelian |
true
|
| gptkbp:A_3_is_isomorphic_to |
cyclic group of order 3
|
| gptkbp:A_4_has_normal_subgroup |
gptkb:Klein_four-group
|
| gptkbp:A_4_is_isomorphic_to |
group of even permutations on 4 elements
|
| gptkbp:A_4_is_not_simple |
true
|
| gptkbp:A_4_is_solvable |
true
|
| gptkbp:A_5_is_isomorphic_to |
gptkb:icosahedral_group
|
| gptkbp:A_5_is_not_solvable |
true
|
| gptkbp:A_5_is_simple |
true
|
| gptkbp:A_5_is_smallest_non-abelian_simple_group |
true
|
| gptkbp:A_6_has_outer_automorphism |
true
|
| gptkbp:A_n_is_abelian_for |
n <= 3
|
| gptkbp:A_n_is_centerless_for |
n >= 3
|
| gptkbp:A_n_is_finite_group |
true
|
| gptkbp:A_n_is_generated_by |
3-cycles
|
| gptkbp:A_n_is_index_2_subgroup_of |
gptkb:S_n
|
| gptkbp:A_n_is_maximal_subgroup_of_S_n_for |
n >= 5
|
| gptkbp:A_n_is_non-abelian_for |
n >= 4
|
| gptkbp:A_n_is_non-cyclic_for |
n >= 4
|
| gptkbp:A_n_is_nontrivial_for |
n >= 3
|
| gptkbp:A_n_is_not_complete_for |
n = 6
|
| gptkbp:A_n_is_not_solvable_for |
n >= 5
|
| gptkbp:A_n_is_perfect_for |
n >= 5
|
| gptkbp:A_n_is_simple_for |
n >= 5
|
| gptkbp:A_n_is_transitive_group |
true
|
| gptkbp:A_n_is_used_in |
gptkb:algebra
gptkb:geometry gptkb:Galois_theory combinatorics finite simple groups classification theory of equations |
| gptkbp:affiliatedWith |
Imperial government
|
| gptkbp:alsoKnownAs |
gptkb:Syffim_(in_Hammerfell)
|
| gptkbp:alternativeName |
group
guild Fighters_Guild Finite_simple_group Group Group_of_people Gruppentheorie Guild Matrix_group Social_group alternating_group animal_group castellers_group finite_group finite_simple_group group_(mathematics) group_of_actors group_of_artists group_of_astronauts group_of_athletes group_of_historical_figures group_of_individuals group_of_philosophers group_of_poets group_of_politicians group_of_scholars group_of_students group_of_writers groupware mathematical_group matrix matrix_group social_group symmetric_group user_group קבוצת_אנשים 団体 |
| gptkbp:appearsIn |
gptkb:The_Elder_Scrolls_III:_Morrowind
gptkb:The_Elder_Scrolls_II:_Daggerfall gptkb:The_Elder_Scrolls_Online gptkb:The_Elder_Scrolls_series gptkb:The_Elder_Scrolls_IV:_Oblivion |
| gptkbp:application |
gptkb:Computer_graphics
gptkb:Physics gptkb:geometry gptkb:robot gptkb:signal_processing gptkb:Graph_theory gptkb:Number_theory gptkb:Topology gptkb:Crystallography gptkb:Galois_theory gptkb:Game_theory gptkb:Control_theory gptkb:Differential_equations gptkb:Quantum_mechanics Chemistry Economics cryptography physics representation theory Statistics Cryptography Machine learning Mathematical physics Combinatorics Coding theory Dynamical systems Network theory Algebraic combinatorics Symmetry in mathematics |
| gptkbp:beschäftigt_sich_mit |
gptkb:Gruppen
|
| gptkbp:class |
26 sporadic simple groups
Alternating groups of degree at least 5 Cyclic groups of prime order Finite simple groups of Lie type Classified by the classification of finite simple groups |
| gptkbp:commonIn |
Medieval towns
|
| gptkbp:contains |
Gruppenordnung
Normalteiler Darstellungstheorie Gruppenaktionen Gruppenautomorphismen Gruppenaxiome Gruppenisomorphismen Klassengleichung Lie-Gruppen Matrixgruppen Permutationsgruppen Quotientengruppen Sylow-Sätze Untergruppen abelsche Gruppen endliche Gruppen nichtabelsche Gruppen symmetrische Gruppen unendliche Gruppen zyklische Gruppen |
| gptkbp:containsElement |
identity element
inverse element group element |
| gptkbp:declinedAfter |
gptkb:Industrial_Revolution
Rise of capitalism |
| gptkbp:definedIn |
A set of invertible matrices over a field or ring, closed under matrix multiplication and inversion
|
| gptkbp:defines |
An association of artisans or merchants who oversee the practice of their craft/trade in a particular area
the group of even permutations of n elements a set of invertible matrices over a field or ring, closed under matrix multiplication and inversion set with a binary operation satisfying group axioms A nontrivial finite group whose only normal subgroups are the trivial group and itself |
| gptkbp:dissolved |
Early modern period (varied by region)
|
| gptkbp:etymology |
From Old English 'gild', meaning payment or tribute
|
| gptkbp:example |
gptkb:general_linear_group
gptkb:Orthogonal_group gptkb:Special_linear_group gptkb:Symplectic_group gptkb:Unitary_group gptkb:Bakers'_guild gptkb:Blacksmiths'_guild gptkb:Merchant_guild gptkb:Weavers'_guild orthogonal group General linear group |
| gptkbp:explores |
Gruppenhomomorphismen
Gruppenoperationen |
| gptkbp:field |
gptkb:mathematics
gptkb:Group_theory gptkb:Abstract_algebra abstract algebra group theory |
| gptkbp:first_classified |
20th century
|
| gptkbp:first_nontrivial_example |
gptkb:A_3
|
| gptkbp:foundedBy |
Versidue-Shaie (according to lore)
|
| gptkbp:foundedIn |
gptkb:Tamriel
|
| gptkbp:founder |
gptkb:Évariste_Galois
gptkb:Camille_Jordan gptkb:Sophus_Lie gptkb:Arthur_Cayley |
| gptkbp:governedBy |
Guild charter
|
| gptkbp:hasApplication |
gptkb:algebraic_geometry
gptkb:geometry gptkb:music gptkb:topology gptkb:symmetry gptkb:Galois_theory gptkb:Algebraische_Geometrie gptkb:Graphentheorie chemistry coding theory cryptography crystallography differential geometry dynamical systems error-correcting codes number theory physics quantum mechanics representation theory robotics theoretical computer science combinatorics graph theory knot theory Quantenmechanik Codierungstheorie Galoistheorie Kombinatorik Kristallographie Symmetrieanalyse Fehlerkorrektur Knoten- und Flächentheorie Molekülstruktur |
| gptkbp:hasAxiom |
associativity
identity element closure inverse element |
| gptkbp:hasInvariant |
gptkb:fictional_character
gptkb:knowledge_representation gptkb:Sylow_subgroup composition series group cohomology normal subgroup automorphism group inner automorphism group outer automorphism group Frattini subgroup commutator subgroup conjugacy class coset derived series group action group extension index of subgroup group homomorphism group isomorphism center of group order of element order of group socle |
| gptkbp:hasProperty |
invertible
associative closed under operation has identity |
| gptkbp:hasSubgroup |
gptkb:group_of_people
gptkb:Orthogonal_group gptkb:Special_linear_group gptkb:Symplectic_group gptkb:Unitary_group |
| gptkbp:hasSupergroup |
General linear group
|
| gptkbp:hasSuperstructure |
gptkb:King
finite field monoid |
| gptkbp:hasType |
gptkb:general_linear_group
gptkb:Klein_four-group gptkb:group_of_people gptkb:topology gptkb:Heisenberg_group gptkb:Lie_group abelian group dihedral group modular group orthogonal group trivial group free group infinite cyclic group p-group profinite group automorphism group simple group cyclic group permutation group quotient group semidirect product solvable group infinite group locally finite group nilpotent group projective group torsion group finite cyclic group direct product of groups |
| gptkbp:headquartersLocation |
varies by game
|
| https://www.w3.org/2000/01/rdf-schema#label |
group of people
|
| gptkbp:importantFor |
Building blocks of all finite groups
|
| gptkbp:influencedBy |
gptkb:church
gptkb:local_government Monarchs |
| gptkbp:is_normal_subgroup_of |
gptkb:group_of_people
|
| gptkbp:is_not_simple_for |
n = 1, 2, 3, 4
|
| gptkbp:is_simple_group_for |
n >= 5
|
| gptkbp:language |
English
|
| gptkbp:leader |
varies by game
|
| gptkbp:legacy |
gptkb:Livery_companies_in_London
Trade unions Modern professional associations |
| gptkbp:mainActivity |
monster hunting
mercenary work protection services |
| gptkbp:meetingPlace |
gptkb:Guildhall
|
| gptkbp:members |
Masters
Apprentices Journeymen |
| gptkbp:membership |
combat skills
loyalty to guild |
| gptkbp:motto |
For the good of all
|
| gptkbp:notableExample |
gptkb:Creature
Cyclic group of order 2 Alternating group A5 |
| gptkbp:notableMember |
gptkb:Modryn_Oreyn
gptkb:Sees-All-Colors gptkb:Vilena_Donton Percius Mercius |
| gptkbp:notablePerson |
gptkb:Richard_Brauer
gptkb:John_G._Thompson gptkb:Michael_Aschbacher gptkb:Robert_Griess gptkb:Daniel_Gorenstein |
| gptkbp:notation |
A_n
|
| gptkbp:number_of_types |
Four infinite families and 26 sporadic groups
|
| gptkbp:operator |
matrix multiplication
Matrix multiplication group operation |
| gptkbp:order |
n!/2
|
| gptkbp:originatedIn |
Medieval Europe
|
| gptkbp:parentOrganization |
none
|
| gptkbp:property |
gptkb:Closure
associativity Associativity contains the identity matrix every element has an inverse Identity element Inverse element Has no nontrivial normal subgroups |
| gptkbp:purpose |
Control prices
Protect members Provide training and apprenticeships Regulate trade Set standards for quality |
| gptkbp:regulates |
Guild regulations
|
| gptkbp:related_theorem |
gptkb:Jordan–Hölder_theorem
Classification theorem of finite simple groups |
| gptkbp:relatedConcept |
gptkb:Alternating_group
gptkb:Suzuki_group gptkb:Weyl_group gptkb:Conway_group gptkb:Creature gptkb:Lie_group gptkb:Thompson_group gptkb:Composition_series gptkb:Lyons_group gptkb:Harada–Norton_group gptkb:Held_group gptkb:O'Nan_group gptkb:Rudvalis_group orthogonal group Group homomorphism Automorphism group group homomorphism Lie type group Simple group Baby Monster group Group action Normal subgroup Cyclic group Fischer group Janko group Sporadic group |
| gptkbp:relatedTo |
gptkb:trade_unionist
Craftsmanship Livery company Apprenticeship Group homomorphism Automorphism group Group action Linear transformation |
| gptkbp:rival |
gptkb:Dark_Brotherhood
gptkb:Thieves_Guild |
| gptkbp:studiedIn |
gptkb:Lie_theory
gptkb:Linear_algebra gptkb:Representation_theory abstract algebra |
| gptkbp:subunit |
subfamily
|
| gptkbp:symbol |
gptkb:coat_of_arms
A_n |
| gptkbp:used_in |
gptkb:geometry
gptkb:topology gptkb:Zahlentheorie gptkb:Chemie Informatik Physik Kryptographie |
| gptkbp:bfsParent |
gptkb:Xerox_PARC_researchers
|
| gptkbp:bfsLayer |
3
|