Nilpotent group
type: Ontology
creation date: 2025-11-03T08:11:41+00:00
imports: http://semantic-mediawiki.org/swivt/1.0

Nilpotent group
type: Subject
type: Category:Semi-basic definitions in group theory
type: Category:Group properties
type: Category:Pivotal group properties
type: Category:Pages with math errors
type: Category:GAP-testable group properties
type: Category:Standard terminology
type: Category:Pages with math render errors
page: https://groupprops.subwiki.org/wiki/Nilpotent_group
wiki namespace: 0
wiki page content language: en
defining ingredient: Commutator of two subgroups
defining ingredient: Subnormal subgroup
defining ingredient: Center
defining ingredient: Lower central series
defining ingredient: Square of a group
defining ingredient: Commutator
defining ingredient: Diagonal-in-square operator
definition style: tabular
dissatisfies metaproperty: Extension-closed group property
importance rank: 2
MSC class: 20F18
obtained by applying: Diagonal-in-square operator
page class: Term
satisfies metaproperty: Finite direct product-closed group property
satisfies metaproperty: Subgroup-closed group property
satisfies metaproperty: Quotient-closed group property
satisfies metaproperty: Pseudovarietal group property
satisfies metaproperty: Finite normal join-closed group property
satisfies metaproperty: Isoclinism-invariant group property
stronger than: Solvable group
stronger than: Metanilpotent group
stronger than: Group in which every maximal subgroup is normal
stronger than: Group in which every subgroup is subnormal
stronger than: Group satisfying normalizer condition
stronger than: Gruenberg group
stronger than: Hypercentral group
stronger than: Hypocentral group
stronger than: Locally nilpotent group
stronger than: Residually nilpotent group
stronger than: N-nilpotent group
weaker than: Abelian group
weaker than: Cyclic group
weaker than: Group of nilpotency class two
weaker than: Finitely generated nilpotent group
weaker than: Finite nilpotent group
weaker than: Periodic nilpotent group
weaker than: Divisible nilpotent group
weaker than: Nilpotent group that is divisible for a set of primes
weaker than: Rationally powered nilpotent group
weaker than: Torsion-free nilpotent group
weaker than: Nilpotent group that is torsion-free for a set of primes
weaker than: Group of prime power order
weaker than: Group whose automorphism group is nilpotent
weaker than: UL-equivalent group
wiki page modification date: 2021-12-27T02:11:46Z
modification date#aux: 2459575.5915046
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query string: Hypercentral group Nilpotent group
wiki page sort key: Nilpotent group# QUERY701d28602f4685823217bb05bba37aef

http://groupprops.subwiki.org/wiki/Special:URIResolver/Nilpotent_group-23_QUERYaec43483871e5ccad290228a8998cd15
type: Subject
master page: Nilpotent group
wiki namespace: 0
query depth: 1
query format: list
query size: 4
query string: Hypocentral group Nilpotent group
wiki page sort key: Nilpotent group# QUERYaec43483871e5ccad290228a8998cd15

http://groupprops.subwiki.org/wiki/Special:URIResolver/Nilpotent_group-23_QUERY82c9525859b8f9e61007547960b7e3a2
type: Subject
master page: Nilpotent group
wiki namespace: 0
query depth: 1
query format: broadtable
query size: 4
query string: Hypocentral group Nilpotent group
wiki page sort key: Nilpotent group# QUERY82c9525859b8f9e61007547960b7e3a2

http://groupprops.subwiki.org/wiki/Special:URIResolver/Nilpotent_group-23_QUERY80f9e0984940d64550bba7a2b3794e71
type: Subject
master page: Nilpotent group
wiki namespace: 0
query depth: 1
query format: list
query size: 4
query string: Locally nilpotent group Nilpotent group
wiki page sort key: Nilpotent group# QUERY80f9e0984940d64550bba7a2b3794e71

http://groupprops.subwiki.org/wiki/Special:URIResolver/Nilpotent_group-23_QUERY45b2fe463e48916d600a238ea9629e36
type: Subject
master page: Nilpotent group
wiki namespace: 0
query depth: 1
query format: broadtable
query size: 4
query string: Locally nilpotent group Nilpotent group
wiki page sort key: Nilpotent group# QUERY45b2fe463e48916d600a238ea9629e36

http://groupprops.subwiki.org/wiki/Special:URIResolver/Nilpotent_group-23_QUERYe47df42365db2b7c105fb2f7671fba6c
type: Subject
master page: Nilpotent group
wiki namespace: 0
query depth: 1
query format: list
query size: 4
query string: Residually nilpotent group Nilpotent group
wiki page sort key: Nilpotent group# QUERYe47df42365db2b7c105fb2f7671fba6c

http://groupprops.subwiki.org/wiki/Special:URIResolver/Nilpotent_group-23_QUERY9a2e4b3e1f3023941925cc61ffe231a0
type: Subject
master page: Nilpotent group
wiki namespace: 0
query depth: 1
query format: broadtable
query size: 4
query string: Residually nilpotent group Nilpotent group
wiki page sort key: Nilpotent group# QUERY9a2e4b3e1f3023941925cc61ffe231a0

http://groupprops.subwiki.org/wiki/Special:URIResolver/Nilpotent_group-23_QUERYa1136ba471c50b97991562a8e87bef2a
type: Subject
master page: Nilpotent group
wiki namespace: 0
query depth: 1
query format: plainlist
query size: 2
query string: Diagonal-in-square operator
wiki page sort key: Nilpotent group# QUERYa1136ba471c50b97991562a8e87bef2a

Symmetric group:S3
type: Subject
page: https://groupprops.subwiki.org/wiki/Symmetric_group-3AS3
wiki namespace: 0
wiki page content language: en
dissatisfies property: Nilpotent group
wiki page sort key: Symmetric group:S3

Direct product of Z5 and S3
type: Subject
page: https://groupprops.subwiki.org/wiki/Direct_product_of_Z5_and_S3
wiki namespace: 0
wiki page content language: en
dissatisfies property: Nilpotent group
wiki page sort key: Direct product of Z5 and S3

Direct product of Z3 and D10
type: Subject
page: https://groupprops.subwiki.org/wiki/Direct_product_of_Z3_and_D10
wiki namespace: 0
wiki page content language: en
dissatisfies property: Nilpotent group
wiki page sort key: Direct product of Z3 and D10

Dihedral group:D14
type: Subject
page: https://groupprops.subwiki.org/wiki/Dihedral_group-3AD14
wiki namespace: 0
wiki page content language: en
dissatisfies property: Nilpotent group
wiki page sort key: Dihedral group:D14

Dihedral group:D22
type: Subject
page: https://groupprops.subwiki.org/wiki/Dihedral_group-3AD22
wiki namespace: 0
wiki page content language: en
dissatisfies property: Nilpotent group
wiki page sort key: Dihedral group:D22

Dihedral group:D26
type: Subject
page: https://groupprops.subwiki.org/wiki/Dihedral_group-3AD26
wiki namespace: 0
wiki page content language: en
dissatisfies property: Nilpotent group
wiki page sort key: Dihedral group:D26

Projective special linear group:PSL(3,2)
type: Subject
page: https://groupprops.subwiki.org/wiki/Projective_special_linear_group-3APSL-283-2C2-29
wiki namespace: 0
wiki page content language: en
dissatisfies property: Nilpotent group
wiki page sort key: Projective special linear group:PSL(3,2)

Alternating group:A4
type: Subject
page: https://groupprops.subwiki.org/wiki/Alternating_group-3AA4
wiki namespace: 0
wiki page content language: en
dissatisfies property: Nilpotent group
wiki page sort key: Alternating group:A4

General affine group:GA(1,11)
type: Subject
page: https://groupprops.subwiki.org/wiki/General_affine_group-3AGA-281-2C11-29
wiki namespace: 0
wiki page content language: en
dissatisfies property: Nilpotent group
wiki page sort key: General affine group:GA(1,11)

Alternating group:A6
type: Subject
page: https://groupprops.subwiki.org/wiki/Alternating_group-3AA6
wiki namespace: 0
wiki page content language: en
dissatisfies property: Nilpotent group
wiki page sort key: Alternating group:A6

Cyclic group:Z2
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ2
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z2

Cyclic group:Z3
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ3
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z3

Elementary abelian group:E25
type: Subject
page: https://groupprops.subwiki.org/wiki/Elementary_abelian_group-3AE25
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Elementary abelian group:E25

Cyclic group:Z30
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ30
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z30

Elementary abelian group:E49
type: Subject
page: https://groupprops.subwiki.org/wiki/Elementary_abelian_group-3AE49
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Elementary abelian group:E49

Quaternion group
type: Subject
page: https://groupprops.subwiki.org/wiki/Quaternion_group
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Quaternion group

Cyclic group:Z71
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ71
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z71

Cyclic group:Z103
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ103
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z103

Cyclic group:Z107
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ107
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z107

Cyclic group:Z113
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ113
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z113

Cyclic group:Z61
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ61
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z61

Cyclic group:Z97
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ97
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z97

Cyclic group:Z73
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ73
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z73

Cyclic group:Z89
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ89
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z89

Cyclic group:Z11
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ11
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z11

Cyclic group:Z13
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ13
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z13

Cyclic group:Z17
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ17
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z17

Cyclic group:Z19
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ19
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z19

Cyclic group:Z23
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ23
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z23

Cyclic group:Z29
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ29
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z29

Cyclic group:Z31
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ31
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z31

Cyclic group:Z37
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ37
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z37

Cyclic group:Z41
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ41
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z41

Cyclic group:Z43
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ43
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z43

Cyclic group:Z47
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ47
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z47

Cyclic group:Z53
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ53
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z53

Cyclic group:Z59
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ59
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z59

Cyclic group:Z67
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ67
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z67

Cyclic group:Z79
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ79
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z79

Cyclic group:Z83
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ83
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z83

Cyclic group:Z28
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group-3AZ28
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Cyclic group:Z28

Direct product of Z2 and Z14
type: Subject
page: https://groupprops.subwiki.org/wiki/Direct_product_of_Z2_and_Z14
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Direct product of Z2 and Z14

Dihedral group:D8
type: Subject
page: https://groupprops.subwiki.org/wiki/Dihedral_group-3AD8
wiki namespace: 0
wiki page content language: en
satisfies property: Nilpotent group
wiki page sort key: Dihedral group:D8

Abelian group
type: Subject
page: https://groupprops.subwiki.org/wiki/Abelian_group
wiki namespace: 0
wiki page content language: en
stronger than: Nilpotent group
wiki page sort key: Abelian group

Cyclic group
type: Subject
page: https://groupprops.subwiki.org/wiki/Cyclic_group
wiki namespace: 0
wiki page content language: en
stronger than: Nilpotent group
wiki page sort key: Cyclic group

Dedekind group
type: Subject
page: https://groupprops.subwiki.org/wiki/Dedekind_group
wiki namespace: 0
wiki page content language: en
stronger than: Nilpotent group
wiki page sort key: Dedekind group

Solvable group
type: Subject
page: https://groupprops.subwiki.org/wiki/Solvable_group
wiki namespace: 0
wiki page content language: en
weaker than: Nilpotent group
wiki page sort key: Solvable group

Engel group
type: Subject
page: https://groupprops.subwiki.org/wiki/Engel_group
wiki namespace: 0
wiki page content language: en
weaker than: Nilpotent group
wiki page sort key: Engel group

Dissatisfies property
type: ObjectProperty
page: https://groupprops.subwiki.org/wiki/Property-3ADissatisfies_property
wiki namespace: 132
wiki page content language: en
wiki page sort key: Dissatisfies property
type: wpg

Satisfies property
type: ObjectProperty
page: https://groupprops.subwiki.org/wiki/Property-3ASatisfies_property
wiki namespace: 132
wiki page content language: en
wiki page sort key: Satisfies property
type: wpg

Stronger than
type: ObjectProperty
page: https://groupprops.subwiki.org/wiki/Property-3AStronger_than
wiki namespace: 132
wiki page content language: en
wiki page sort key: Stronger than

Weaker than
type: ObjectProperty
page: https://groupprops.subwiki.org/wiki/Property-3AWeaker_than
wiki namespace: 132
wiki page content language: en
wiki page sort key: Weaker than